
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 a circle $C$ whose center is the intersection point of the line $x-y+2=0$ and the $x$-axis, and circle $C$ is externally tangent to the circle $(x-2)^{2}+(y-3)^{2}=9$, if a line $l$ passing through point $P(-1,1)$ intersects circle $C$ at points $A$ and $B$, when $\angle ACB$ is minimized, the equation of line $l$ is \_\_\_\_\_\_.

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