
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
Triangle \(ABC\) is isosceles with \(AB = AC\) and \(BC = 65 \, \text{cm}\). \(P\) is a point on \(BC\) such that the perpendicular distances from \(P\) to \(AB\) and \(AC\) are \(24 \, \text{cm}\) and \(36 \, \text{cm}\), respectively. Find the area of \(\triangle ABC\).

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