
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
If \( P \) is an arbitrary point in the interior of the equilateral triangle \( ABC \), find the probability that the area of \( \triangle ABP \) is greater than each of the areas of \( \triangle ACP \) and \( \triangle BCP \).

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