
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 \( \triangle ABC \), \( \angle ACB = \frac{\pi}{2} \), \( AC = BC = 2 \), and point \( P \) lies on the hypotenuse \( AB \), with \( BP = 2PA \). Determine the value of \( \overrightarrow{CP} \cdot \overrightarrow{CA} + \overrightarrow{CP} \cdot \overrightarrow{CB} \).

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