
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
Triangle  $ABC$  has right angle  $A$ , with  $AB=AC=6$ . Point  $P$  is located within triangle  $ABC$  such that the areas of triangles  $ABP$ ,  $BCP$ , and  $ACP$  are equal. Express  $CP$  in simplest radical form.

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