
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 circle $⊙C$: $((x-1)^{2}+(y-2)^{2}=2)$, and point $P(2,-1)$, draw a tangent line through point $P$, with the points of tangency being $A$ and $B$.

(1) Find the equations of the lines $PA$ and $PB$;
(2) Find the length of the tangent line through point $P$.

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