
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, tangents PA and PB are drawn from a moving point P to the circles $C_1: x^2+y^2-4x-6y+9=0$ and $C_2: x^2+y^2+2x+2y+1=0$ respectively. Given that $|PA|=|PB|$ and O is the origin, calculate the minimum value of $|OP|$.

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