
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 the right triangle \( \triangle ABC \), the hypotenuse \( AB = 5 \), the leg \( AC = 3 \). The angle bisector of \( \angle A \) intersects the opposite side at \( A_1 \). A second right triangle \( \triangle PQR \) is formed such that \( PQ = A_1B \), and \( PR = A_1C \). If the angle bisector of \( \angle P \) intersects the opposite side at \( P_1 \), calculate the length of \( PP_1 \).

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