What does Haymitch Abernathy convince Seneca to do?

In Suzanne Collins's "The Hunger Games," Haymitch Abernathy doesn't convince Seneca Crane, the Head Gamemaker, to do anything directly. However, Haymitch's actions and influence indirectly lead to Seneca's demise.

Here's how:

* Haymitch manipulates the Gamemakers: He subtly guides the Gamemakers into making decisions that benefit Katniss and Peeta, especially during the "forbidden fruit" scene. He does this through his drunken ramblings and clever suggestions.

* Haymitch's plan leads to the berries: The manipulation leads the Gamemakers to believe that Katniss and Peeta are planning a mass suicide. Their decision to allow the berries is a direct result of Haymitch's machinations.

* Seneca's decision to allow the berries: Seneca, as Head Gamemaker, ultimately authorizes the berries, defying the Capitol's rules and ultimately costing him his life. The Capitol, enraged by this act of defiance, executes him.

Therefore, while Haymitch doesn't directly convince Seneca to do anything, his actions and influence lead Seneca to make the fateful decision that ultimately seals his fate.