
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
A ray of light $l$ is emitted from point $P(-6, 7)$ and reflects off the x-axis. The line of the reflected ray is tangent to the circle $x^2+y^2-8x-6y+21=0$.  
(1) Find the equation of the line of the ray $l$.  
(2) Find the distance traveled by the ray from point $P$ to the tangent point.

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