
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
In any isosceles triangle \(PQR\) with \(PQ = PR\), the altitude \(PS\) bisects the base \(QR\) so that \(QS = SR\). Given \(PQ = PR = 15\) and \(QR = 20\), determine the area of \(\triangle PQR\).

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