In truth, the President must express his sincerity to the people by late September or early October...

In truth, President Lee Jae-myung needs to deliver a public address to the nation by late September (around the Chuseok holiday) or early October. If this window is missed, approval ratings will drop into the 22%–25% range by December. Once it hits that point, he will have to step down immediately.
In particular, it must be kept in mind that approval ratings among those in their 20s are in the 10% range.
Actually, I believed that if the Yoon Suk-yeol administration had issued a public apology and reflected on its actions around April 2024, it could have lasted until the end of its term. At that time, the Blue House was likely in a position where a problem had already occurred, making it impossible to apologize.
The Lee Jae-myung administration is currently at this very juncture. If this timing is missed and a public address is made in December when approval ratings are at 22%–25%, recovery will no longer be possible. There is a high possibility he will have to leave office. This is because it is the second year of the administration—in other words, just over a year and a half into the term—and the problems are significant.
There is only one way right now. He must express his sincerity to the people. He has earned the people's suspicion. In other words, the people have lost trust in the state administration. This also involves a problem with presidential leadership.
Around December, citizens may actually take to the streets and some protests may occur. While these protests might not be intense initially, if this period is not managed, the protests will become truly violent. Protests by those in their 20s, in particular, will intensify. They will take to the streets.
The role of the Democratic Party of Korea will be important at this time, but in reality, internal strife is occurring within the Democratic Party. The fact that the Democratic Party holds 180 seats will become a major problem. While citizens already desire impeachment, the Democratic Party's 180 seats will pose a significant issue, and at this point, they could follow in the footsteps of the late Roh Moo-hyun.
He could certainly make it until the third year of his term, but if he fails to pass this point, he could have been a hero president, but instead, there is a possibility he will become a failed president. Now is the critical moment when this can be resolved.
In other words, historically, he will be left with the title of "the president who neglected and ignored the will of the people."
PS) I am certain. It seems it will turn out this way.