
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 \(ABC\) be a triangle with \(AB = 13\), \(BC = 14\), and \(CA = 15\). Suppose \(PQRS\) is a square such that \(P\) and \(R\) lie on line \(BC\), \(Q\) lies on line \(CA\), and \(S\) lies on line \(AB\). Compute the side length of this square.

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