Canto 3 -
Araṇya-kāṇḍa
Chapter 64: Rāma Discovers Some Clues About Sītā’s Whereabouts
Text 3.64.24

बाढमित्येव काकुत्स्थः प्रस्थितो दक्षिणां दिशम्।
लक्ष्मणानुगतः श्रीमान्वीक्षमाणो वसुन्धराम्॥

bāḍham ity eva kākutsthaḥ prasthito dakṣiṇāṁ diśam
lakṣmaṇānugataḥ śrīmān vīkṣamāṇo vasundharām

bāḍham iti eva = saying “alright”; kākutsthaḥ = Kākutstha; prasthitaḥ = set out; dakṣiṇām = in the southern; diśam = direction; lakṣmaṇa-anugataḥ = followed by Lakṣmaṇa; śrīmān = prosperous; vīkṣamāṇaḥ = while examining; vasundharām = the ground.

[Saying] “Alright,” prosperous Kākutstha, followed by Lakṣmaṇa, set out in the southern direction while examining the ground.

Lord Rāma was prosperous, that is, He was filled with the prosperity of having discovered the means to find out Sītā-devī.1

1 Śrī Rāma’s discovery of the means to find out Sītā-devī was His prosperity at that point in time. Therefore, Śrī Vālmīki Maharṣi has described Him as “prosperous Kākutstha.”