
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 Cartesian coordinate system, two tangent lines are drawn through point $P(3,0)$ to circle $O:{(x-1)^2}+{(y-2\sqrt{3})^2}=4$, with tangency points $A$ and $B$. Derive the equation of line $AB$.

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