
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
A point \( P \) is chosen at random in the interior of an isosceles triangle \( ABC \) where \( AB = AC \). What is the probability that \( \triangle ABP \) has a smaller area than each of \( \triangle ACP \) and \( \triangle BCP \)?

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