
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
Let the center of the circle $x^{2}+y^{2}-2x-2y-2=0$ be $C$, and the line $l$ passes through $(2,3)$ and intersects the circle $C$ at points $A$ and $B$. If $|{AB}|=2\sqrt{3}$, then the equation of line $l$ is ____.

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