
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 emitted from point A($-3$, $3$) strikes the x-axis and is reflected. The line of the reflected ray is tangent to the circle C: $x^2 + y^2 - 4x - 4y + 7 = 0$. Determine:
(1) The equations of the ray of light $\ell$ and the line of the reflected ray;
(2) The distance traveled by the ray of light from point A to the tangent point.

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