
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 \(ABCD\) be a convex trapezoid such that \(\angle BAD = \angle ADC = 90^{\circ}\), \(AB = 20\), \(AD = 21\), and \(CD = 28\). Point \(P \neq A\) is chosen on segment \(AC\) such that \(\angle BPD = 90^{\circ}\). Compute \(AP\).

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