
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 rectangular coordinate system on a plane, a line $PA$ is tangent to the circle $C\_1$: $x^{2}+y^{2}-4x-6y+9=0$ and a line $PB$ is tangent to the circle $C\_2$: $x^{2}+y^{2}+2x+2y+1=0$, where $P$ is a moving point, and $A$ and $B$ are the points of tangency. If $|PA|=|PB|$, and $O$ is the origin, find the minimum value of $|OP|$.

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