
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]


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Let \( AB \) and \( CD \) be perpendicular segments intersecting at point \( P \). Suppose that \( AP = 2 \), \( BP = 3 \), and \( CP = 1 \). If all the points \( A \), \( B \), \( C \), and \( D \) lie on a circle, find the length of \( DP \).

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