
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 the line $l$: $y=2x$, a point $P$ on it forms a circle $C$: $(x-8)^{2}+(y-1)^{2}=2$. The tangents $l_{1}$, $l_{2}$ from point $P$ to the circle are symmetric about line $l$. Find the distance from point $P$ to the center of circle $C$.

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