
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 $P$ is any point on the ellipse $\frac{x^2}{4}+y^2=1$ ($y\neq-1$), two tangents $PM$ and $PN$ are drawn from $P$ to the circle $C: x^{2}+(y+2)^{2}=1$, with tangents intersecting at $M$ and $N$. Find the minimum value of $\overrightarrow{CM} \cdot \overrightarrow{CN}$.

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