Being a reservoir of all auspicious attributes, Śrī Advaita Ācārya is all-auspicious for the world. His characteristics, activities and name are always auspicious.
Śrī Advaita Prabhu, who is an incarnation of Mahā-Viṣṇu, is an ācārya, or teacher. All His activities and all the other activities of Viṣṇu are auspicious. Anyone who can view the all-auspiciousness in the pastimes of Lord Viṣṇu also becomes auspicious simultaneously. Therefore, since Lord Viṣṇu is the fountainhead of auspiciousness, anyone who is attracted by the devotional service of Lord Viṣṇu can render the greatest service to human society. Rejected persons of the material world who refuse to understand pure devotional service as the eternal function of the living entities, and as actual liberation of the living being from conditioned life, become bereft of all devotional service because of their poor fund of knowledge.
In the teachings of Advaita Prabhu there is no question of fruitive activities or impersonal liberation. Bewildered by the spell of the material energy, however, persons who could not understand that Advaita Prabhu is nondifferent from Viṣṇu wanted to follow Him with their impersonal conceptions. The attempt of Advaita Prabhu to punish them is also auspicious. LordViṣṇu and His activities can bestow all good fortune, directly and indirectly. In other words, being favored by Lord Viṣṇu and being punished by Lord Viṣṇu are one and the same because all the activities of Viṣṇu are absolute. According to some, Maṅgala was another name of Advaita Prabhu. As the causal incarnation, or Lord Viṣṇu's incarnation for a particular occasion, He is the supply agent or ingredient in material nature. However, He is never to be considered material. All His activities are spiritual. Anyone who hears about and glorifies Him becomes glorified himself, for such activities free one from all kinds of misfortune. One should not invest any material contamination or impersonalism in the Viṣṇu form. Everyone should try to understand the real identity of Lord Viṣṇu, for by such knowledge one can attain the highest stage of perfection.
(Sri Caitanya Caritamrta----1:6:12--- translation and purport).

Although Śrī Advaita Prabhu is an incarnation of Viṣṇu, for the welfare of the conditioned souls He manifested Himself as a servitor of the Supreme Personality of Godhead, and throughout all His activities He showed Himself to be an eternal servitor. Lord Caitanya and Lord Nityānanda also manifested the same principle, although They also belong to the category of Viṣṇu. If Lord Caitanya, Lord Nityānanda and Advaita Prabhu had exhibited Their all-powerful Viṣṇu potencies within this material world, people would have become greater impersonalists, monists and self-worshipers than they had already become under the spell of this age. Therefore the Personality of Godhead and His different incarnations and forms played the parts of devotees to instruct the conditioned souls how to approach the transcendental stage of devotional service. Advaita Ācārya especially intended to teach the conditioned souls about devotional service. The word ācārya means "teacher." The special function of such a teacher is to make people Kṛṣṇa conscious. A bona fide teacher following in the footsteps of Advaita Ācārya has no other business than to spread the principles of Kṛṣṇa consciousness all over the world. The real qualification of an ācārya is that he presents himself as a servant of the Supreme. Such a bona fide ācārya can never support the demoniac activities of atheistic men who present themselves as God. It is the main business of an ācārya to defy such imposters posing as God before the innocent public.
(Sri Caitanya Caritamrta----1:6:12--- purport).

The original bhakta-avatāra is Saṅkarṣaṇa. Śrī Advaita is counted among such incarnations.
Although Śrī Advaita Prabhu belongs to the Viṣṇu category, He displays servitorship to Lord Caitanya Mahāprabhu as one of His associates. When Lord Viṣṇu appears as a servitor, He is called an incarnation of a devotee of Lord Kṛṣṇa. Śrī Saṅkarṣaṇa, who is an incarnation of Viṣṇu in the spiritual sky known as the greater Vaikuṇṭha, is the chief of the quadruple incarnations and is the original incarnation of a devotee. Lord Mahā-Viṣṇu, who is lying on the Causal Ocean, is a manifestation of Saṅkarṣaṇa. He is the original Personality of Godhead who glances over the material and efficient causes of the cosmic manifestation. Advaita Prabhu is accepted as an incarnation of Mahā-Viṣṇu. All the plenary manifestations of Saṅkarṣaṇa are indirect expansions of Lord Kṛṣṇa. That consideration also makes Advaita Prabhu an eternal servitor of Gaura Kṛṣṇa. Therefore He is accepted as a devotee incarnation.
(Sri Caitanya Caritamrta----6:11:12--- translation and purport).

In his Anubhāṣya commentary Śrī Bhaktisiddhānta Sarasvatī Ṭhākura describes the Pañca-tattva as follows: The supreme energetic, the Personality of Godhead, manifesting in order to enjoy five kinds of pastimes, appears as the members of the Pañca-tattva. Actually there is no difference between them because they are situated on the absolute platform, but they manifest different spiritual varieties as a challenge to the impersonalists to taste different kinds of spiritual humors (rasas). In the Vedas it is said, parāsya śaktir vividhaiva śrūyate: (CC.2:13:65, purport) "The varieties of energy of the Supreme Personality of Godhead are differently known." From this statement of the Vedas one can understand that there are eternal varieties of humors, or tastes, in the spiritual world. Śrī Gaurāṅga, Śrī Nityānanda, Śrī Advaita, Śrī Gadādhara and Śrīvāsa Ṭhākura are all on the same platform, but in spiritually distinguishing between them one should understand that Śrī Caitanya Mahāprabhu is the form of a devotee, Nityānanda Prabhu appears in the form of a devotee's spiritual master, AdvaitaPrabhu is the form of a bhakta (devotee) incarnation, Gadādhara Prabhu is the energy of a bhakta, and Śrīvāsa Ṭhākura is a pure devotee. Thus there are spiritual distinctions between them. The bhakta-rūpa (Śrī Caitanya Mahāprabhu), the bhakta-svarūpa (Śrī Nityānanda Prabhu) and the bhakta-avatāra (Śrī Advaita Prabhu) are described as the Supreme Personality of Godhead Himself, His immediate manifestation and His plenary expansion, and They all belong to the Viṣṇu category. Although the spiritual and marginal energies of the Supreme Personality of Godhead are nondifferent from the Supreme Personality of Godhead Viṣṇu, they are predominated subjects, whereas Lord Viṣṇu is the predominator. As such, although they are on the same platform, they have appeared differently in order to facilitate tasting of transcendental mellows. Actually, however, there is no possibility of one being different from the other, for the worshiper and the worshipable cannot be separated at any stage. On the absolute platform, one cannot be understood without the other.
(Sri Caitanya Caritamrta----1:7:5---- purport).

Lord Advaita Ācārya is the incarnation of Mahā-Viṣṇu, whose main function is to create the cosmic world through the actions of māyā.
(Sri Caitanya Caritamrta---1:1:12---translation).

Because He is nondifferent from Hari, the Supreme Lord, He is called Advaita, and because He propagates the cult of devotion, He is called Ācārya. He is the Lord and the incarnation of the Lord's devotee. Therefore I take shelter of Him.
(Sri Caitanya Caritamrta---1:1:13---translation).

Advaita Ācārya saw the entire world to be engaged in activities of material piety and impiety, without a trace of devotional service, or Kṛṣṇa consciousness, anywhere. The fact is that in this material world there is no scarcity of anything except Kṛṣṇa consciousness. Material necessities are supplied by the mercy of the Supreme Lord. We sometimes feel scarcity because of our mismanagement, but the real problem is that people are out of touch with Kṛṣṇa consciousness. Everyone is engaged in material sense gratification, but people have no plan for making an ultimate solution to their real problems, namely birth, disease, old age and death. These four material miseries are called bhava-roga, or material diseases. They can be cured only by Kṛṣṇa consciousness. Therefore Kṛṣṇa consciousness is the greatest benediction for human society.
(Sri Caitanya Caritamrta---1:3:97---purport).

Advaita Ācārya Gosvāmī is an incarnation of the Lord as a devotee. His loud calling was the cause for Kṛṣṇa's incarnation.
(Sri Caitanya Caritamrta---1:3:92---translation).

The truth of Advaita Ācārya has been described in two verses. It is said that material nature has two features, namely the material cause and the efficient cause. The efficient causal activities are caused by Mahā-Viṣṇu, and the material causal activities are caused by another form of Mahā-Viṣṇu, known as Advaita. That Advaita, the superintendent of the cosmic manifestation, has descended in the form of Advaita Ācārya to associate with Lord Caitanya. When He is addressed as the servitor of Lord Caitanya, His glories are magnified because unless one is invigorated by this mentality of servitorship one cannot understand the mellows derived from devotional service to the Supreme Lord, Kṛṣṇa.
(Sri Caitanya Caritamrta---1:6--summary).

Mahā-Viṣṇu performs all the functions for the creation of the universes. Śrī Advaita Ācārya is His direct incarnation.
(Sri Caitanya Caritamrta---1:6:7---translation).