
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
In the Cartesian coordinate system, let P be a point that moves such that it can form tangents PA and PB (where A and B are the points of tangency) to the circles C<sub>1</sub>: $x^2 + y^2 + 2x + 2y + 1 = 0$ and C<sub>2</sub>: $x^2 + y^2 - 4x - 6y + 9 = 0$, respectively. If $|PA| = |PB|$, find the minimum value of $|OP|$.

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