
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
An isosceles triangle $PQR$ has $PQ = PR = 5$, and a circle with radius $3$ is tangent to line $PQ$ at a point $X$ and to line $PR$ at a point $Y$. The points $X$ and $Y$ are not necessarily the vertices $Q$ and $R$. Find the area of the circle that passes through the vertices $P$, $Q$, and $R$.

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