
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, such that the tangent line segments $PM$ and $PN$ are equal in length. 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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