
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 a sphere $O$ inscribed in a regular tetrahedron $A-BCD$, where the edge length of the tetrahedron is $2\sqrt{6}$, and line segment $MN$ is a moving diameter of sphere $O$ (with $M$ and $N$ being the endpoints of the diameter), and point $P$ is a moving point on the surface of the regular tetrahedron $A-BCD$, then the maximum value of $\overrightarrow{PM} \cdot \overrightarrow{PN}$ is ____.

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