
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
Given a right triangle \(ABC\) with legs \(AB = 42\) and \(BC = 56\). A circle passing through point \(B\) intersects side \(AB\) at point \(P\), side \(BC\) at point \(Q\), and side \(AC\) at points \(K\) and \(L\). It is known that \(PK = KQ\) and \(QL: PL = 3: 4\). Find \(PQ^2\).

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