
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 $C:(x-2)^2+(y-3)^2=4$ and a point $P(4,-1)$ outside the circle. Draw a line $l$ through point $P$.

(1) Find the equation of line $l$ when it is tangent to the circle $C$.

(2) Find the length of the chord intercepted by the circle $C$ when the slope of line $l$ is ${135}^{0}$.

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