
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 circle $(x^{2}+(y-2)^{2}=4)$, point $A$ is on the line $(x-y-2=0)$. Two tangent lines are drawn from point $A$ to the circle, with tangent points $T_{1}$ and $T_{2}$.
(I) If point $A$ is $(1,-1)$, find the equation of the line $T_{1}T_{2}$;
(II) Find the minimum value of $|AT_{1}|$.

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