
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 two circles C<sub>1</sub>: $(x+\cos\alpha)^2+(y+\sin\alpha)^2=4$ and C<sub>2</sub>: $(x-5\sin\beta)^2+(y-5\cos\beta)^2=1$, where $\alpha,\beta \in [0,2\pi)$, a tangent line MN is drawn to circle C<sub>2</sub> at point M on circle C<sub>1</sub>, with N being the point of tangency. The range of values for $|MN|$ is ______.

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