
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 the plane region
$$
\left\{\begin{array}{l}
x-\sqrt{3} y+4 \geqslant 0, \\
x+\sqrt{3} y+4 \geqslant 0, \\
x \leqslant 2
\end{array}\right.
$$

a circle is inscribed, and the circle with the largest area is denoted as $\odot M$.
(1) Find the equation of $\odot M$;
(2) $\odot M$ intersects the $x$-axis at points $A$ and $B$. For a moving point $P$ inside the circle such that $|PA|$, $|PM|$, and $|PB|$ form a geometric sequence, find the range of values for $\overrightarrow{PA} \cdot \overrightarrow{PB}$.

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