
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Let $\triangle ABC$ have side lengths $AB=24$, $BC=26$, and $AC=28$. Point $Y$ lies in the interior of $\overline{BC}$, and points $J_1$ and $J_2$ are the incenters of $\triangle ABY$ and $\triangle ACY$, respectively. Find the maximum possible area of $\triangle AJ_1J_2$ as $Y$ varies along $\overline{BC}$.

Present the answer in LaTex format: \boxed{Your answer}
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