
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 $\triangle ABC$ is an equilateral triangle with side length $1$, for any point $M$ in space, let $P$ be a moving point inside (including the boundary) of $\triangle ABC$. The minimum value of $PM$ is defined as the distance from point $M$ to $\triangle ABC$. The volume of the geometric solid formed by points in space that are at a distance not greater than $1$ from $\triangle ABC$ is ______.

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