
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
Consider $\triangle PQR$ with side lengths $PQ = 24$, $QR = 26$, and $PR = 28$. Point $Y$ lies on line segment $QR$. Points $J_1$ and $J_2$ are the incenters of triangles $PQY$ and $PRY$, respectively. Determine the minimum area of triangle $PJ_1J_2$ when $Y$ varies along $QR$.

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