
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
A circle $C: (x-3)^2+(y+1)^2=2$ has two tangent lines passing through a point $P$ on the line $l: y=3x$. If the two tangent lines are symmetric with respect to line $l$, then the distance from point $P$ to the center of circle $C$ is ______.

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