
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 an equilateral triangle $ABC$ with side length $6$, point $D$ is inside the triangle such that $AD = 2$, $BD = 4$, and $CD = 3$. What is the probability that a random point $P$ inside triangle $ABC$ is closer to $D$ than to any vertex $A$, $B$, or $C$?

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