
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 line $l$: $x - y + m = 0$ rotates counterclockwise by $90^{\circ}$ around its intersection with the $x$-axis and passes through point $(2,-3)$.
(1) Find the value of $m$;
(2) Find the equation of the circle that passes through points $A(1,1)$ and $B(2,-2)$ with its center on line $l$.

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