
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 the equation of circle $\odot O$ as $x^{2}+y^{2}=4$ and the equation of circle $\odot M$ as
$$
(x-5 \cos \theta)^{2}+(y-5 \sin \theta)^{2}=1 (\theta \in \mathbf{R}),
$$

Through any point $P$ on $\odot M$, draw two tangents $PE$ and $PF$ to circle $\odot O$, with the tangency points being $E$ and $F$ respectively. Find the minimum value of $\overrightarrow{PE} \cdot \overrightarrow{PF}$.

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