
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 $P(a,b)$ passes through the tangent points $M$ and $N$ on circles $C_1$ and $C_2$ respectively, with $|PM|=|PN|$. Determine the minimum value of $(a^2+b^2-6a-4b+13)$.

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