
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 light ray l from point A $(-3, 3)$ strikes the x-axis and is reflected. The line of the reflected light ray is tangent to the circle M whose equation is $x^2 + y^2 - 4x - 4y + 7 = 0$.
(1) Find the center and radius of circle M;
(2) Find the equation of the circle symmetric to M about the x-axis;
(3) Find the equation of the light ray l.

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