
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: $C_{1}:(x+6)^{2}+(y-5)^{2}=4$ and $C_{2}:(x-2)^{2}+(y-1)^{2}=1$. Let $M$ and $N$ be moving points on circles $C_{1}$ and $C_{2}$ respectively, and let $P$ be a moving point on the x-axis. Find the minimum value of $|PM|+|PN|$.

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