
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 that the center of circle $C$ lies on the line $2x-y-2=0$, and passes through points $A(1,2)$ and $B(2,1)$.  
$(1)$ Find the standard equation of circle $C$;  
$(2)$ If the ray $l$ emitted from point $P(-3,3)$ reflects off the $x$-axis, and the line of the reflected ray is tangent to circle $C$, find the equation of line $l$.

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