
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 triangle $ABC$, $AB = AC = 7$ units, and $BC = 10$ units. Triangle $ABC$ is isosceles with the vertex angle at $A$.

Point $P$ is located inside triangle $ABC$ such that it is twice as far from $B$ as it is from $C$. What is the probability that $P$ is closer to vertex $A$ than to either vertex $B$ or $C$?

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