
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
Given that point  $ P$  is chosen at random in the interior of equilateral triangle  $ ABC$, determine the probability that  $ \triangle ABP$  has a greater area than each of  $ \triangle ACP$  and  $ \triangle BCP$.

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