
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 $\triangle PQR$ have side lengths $PQ=20$, $QR=21$, and $PR=29$. Point $Y$ lies along $\overline{QR}$, and points $J_1$ and $J_2$ are the excenters of $\triangle PQY$ and $\triangle PRY$, respectively, corresponding to the angles at $Y$. Find the maximum possible area of $\triangle PJ_1J_2$ as $Y$ varies along $\overline{QR}$.

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