There is this famous picture depicting Advaita Ācārya worshiping Śālagrāma-śilā to invoke the advent of Śrī Caitanya Mahāprabhu, and this is also widely taught, but this is not correct.
koto dine āilā puṇya gomukhī parbote; tabe gelā śrī gaṇḍakī śālagrāma kṣetre
tahi snāna kori prabhu korilā viśrāma; hari nārāyaṇa nāma jape aviśrāma
dekhi eka śilā cakra sarva-sulakṣaṇa; bhakti kori tāhā loiyā korilā gamana
“After dancing in ecstatic love and offering His obeisances Advaita Ācārya continued to holy Mount Gomukhī and Śrī Gaṇḍakī Śālagrāma Kṣetra, where He bathed and rested. He untiringly performed japa of the holy name of Hari Nārāyaṇa here, and found a Cakra-Śīlā, endowed with all auspicious marks, which He took along with great devotion.”
Caitanya Caritāmṛta (Ādi 3.105-109) describes Advaita Ācārya’s invocation of Śrīman Mahaprabhu as follows –
ei ślokārtha ācārya korena vicāraṇa; kṛṣṇake tulasī-jala deya yei jana
tāra ṛṇa śodhite kṛṣṇa korena cintana - ‘jala-tulasīra sama kichu ghare nāhi dhana’
tabe ātmā veci’ kore ṛṇera śodhana; eta bhāvi’ ācārya korena ārādhana
gaṅgā-jala, tulasī-mañjarī anukṣaṇa; kṛṣṇa-pāda-padma bhāvi’ kore samarpaṇa
kṛṣṇera āhvāna kore koriyā huṅkāra; e-mate kṛṣṇere korāila avatāra
“Advaita Ācārya considered the meaning of the verse in this way: “Not finding any way to repay the debt He owes to one who offers Him a Tulasī-leaf and water, Śrī Kṛṣṇa thinks, ‘There is no wealth in My possession that is equal to a Tulasī-leaf and water.’ Thus the Lord clears the debt by offering Himself to the devotee.” Thinking like this, the Ācārya began worshiping the Lord. Thinking of the lotus feet of Śrī Kṛṣṇa, He constantly offered Tulasī-mañjarīs and Gaṅgā-water, appealing to Śrī Kṛṣṇa with loud roars and thus made it possible for Kṛṣṇa to appear.”
There is no mentioning here of Him worshiping a Śālagrāma-śilā for this purpose. Śrī Caitanya Bhāgavat (Ādi-khaṇḍa 2.78-83) also gives a summary description of the event, also without mentioning Advaita Ācārya worshipping a Śālagrama-śilā.
sei navadvīpe boise vaiṣṇavāgragaṇya; ‘advaita ācārya’ nāma, sarva-loke dhanya
jñāna-bhakti-vairāgyera guru mukhyatara; kṛṣṇa-bhakti vākhānite jeheno śaṅkara
tribhuvane āche joto śāstrera pracāra; sarvatra vākhāne,—’kṛṣṇa-pada-bhakti sāra’
tulasī-mañjarī-sahita gaṅgā-jale; niravadhi seve kṛṣṇe mahā-kutūhale
huṅkāra koroye kṛṣṇa-āveśera teje; ye dhvani brahmāṇḍa bhedi’ vaikuṇṭhete bāje
ye-premera huṅkāra śuniyā kṛṣṇa nātha; bhakti-vaśe āpane ye hoilā sākṣāt
“In that Navadvīpa the leader of all the Vaiṣṇavas, named ‘Advaita ācārya ‘, lived, who was the most blessed in all the worlds. He was the main guru of jñāna (knowledge or wisdom), bhakti (devotion) and vairāgya (renunciation). He was like Śaṅkara (Śiva) in His explanations of Kṛṣṇa-bhakti. He preached all scriptures that existed in the three worlds and explained them all to mean ‘devotion to Kṛṣṇa’s feet is the best’. In great eagerness He always worshiped Kṛṣṇa with Tulasī-mañjarīs and Gaṅgā-water. He roared in a powerful absorption in Kṛṣṇa, and that thunderous sound pierced the shell of the cosmos, resounding in Vaikuṇṭha. When Lord Kṛṣṇa heard these premik roars, He appeared (on earth, as Śrī Caitanya Mahāprabhu), being subdued by (the love of) His devotee.”
Here also, there is no mentioning of Śṛī Advaita-ācārya invoking Śrī Caitanya Mahāprabhu’s advent with a Śālagrāma-śilā. Śṛī Advaita-ācārya’s prāṇa-nātha was Śrī Śrī Rādhā-Madangopāla instead.