The Gītā has 700 verses. Cut them exactly in half and the line falls between verse 350 and verse 351. Those are 9.12 and 9.13.
9.12 describes people who have given themselves to a deluding nature. Their hopes are empty, their actions empty, their knowledge empty.
9.13 begins with one small word: mahātmānas tu. But the great-souled ones, O Arjuna, take shelter in the divine nature and worship me with an undistracted mind.
Tu. But. One syllable in Sanskrit, and the whole book pivots on it. On one side, a life spent chasing what deludes. On the other, a life that turns.
Whether or not anyone planned it, the exact centre of 700 verses is not a command or a doctrine. It is a fork in the road, and a word that lets you choose.
The verses
BHAGAVAD GĪTĀ · 9.12मोघाशा मोघकर्माणो मोघज्ञाना विचेतसः।
राक्षसीमासुरीं चैव प्रकृतिं मोहिनीं श्रिताः।।
moghāśā mogha-karmāṇo mogha-jñānā vicetasaḥ
rākṣasīm āsurīṁ caiva prakṛtiṁ mohinīṁ śritāḥ
Senseless people have a nature that is deluding and similar to that of rakshasas and asuras. Their hopes are futile, their actions are futile, and their knowledge is futile.
BHAGAVAD GĪTĀ · 9.13महात्मानस्तु मां पार्थ दैवीं प्रकृतिमाश्रिताः।
भजन्त्यनन्यमनसो ज्ञात्वा भूतादिमव्ययम्।।
mahātmānas tu māṁ pārtha daivīṁ prakṛtim āśritāḥ
bhajantyananya-manaso jñātvā bhūtādim avyayam
But the great-souled ones, O Arjuna, who are associated with My divine nature, worship Me with an unwavering mind, knowing Me to be the immutable source of all beings.
Going deeper
The story marks the point where the Gītā divides in half. The verse on one side, 9.12, describes people of a deluding nature: their hopes, their actions and their knowledge are all futile. The one before it, 9.11, says that fools disregard him, dwelling in a human form and not knowing his higher nature as Lord of all beings. The verse on the other side, 9.13, begins with a small word, but, and turns to the great-souled, who rely on the divine nature and worship him with an unwavering mind, knowing him as the source of all beings. 9.14 says how: always singing his praise, striving with firm resolve, bowing in devotion. The line between the two verses is a matter of counting, not a statement by the text. What the text itself does at this point is turn from the deluded to the devoted. See chapter 9 and what the Gītā says about devotion.