
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 right triangle \( \triangle ABC \) where \(\angle ACB = 90^\circ\), \(CA = 3\), and \(CB = 4\), there is a point \(P\) inside \(\triangle ABC\) such that the sum of the distances from \(P\) to the three sides is \(\frac{13}{5}\). Find the length of the locus of point \(P\).

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