
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 $C_{1}: x^{2}+y^{2}=4$ and $C_{2}: (x-1)^{2}+(y-3)^{2}=4$, a moving point $P(a, b)$ forms tangents $PM$ and $PN$ with circles $C_{1}$ and $C_{2}$ respectively, where $M$ and $N$ are the points of tangency. If $|PM|=|PN|$, find the minimum value of $a^{2}+b^{2}-6a-4b+13$.

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