
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 $C\_1$: $x^{2}+y^{2}=1$ and $C\_2$: $(x-2)^{2}+(y-4)^{2}=1$, a moving point $P(a,b)$ passes through and forms tangent lines $PM$ and $PN$ to circles $C\_1$ and $C\_2$ respectively with $M$ and $N$ being the points of tangency. If $PM=PN$, find the minimum value of $\sqrt{a^{2}+b^{2}}+\sqrt{(a-5)^{2}+(b+1)^{2}}$.

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