
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
In the Cartesian coordinate plane $(xOy)$, the curve $y=x^{2}-4x+3$ intersects the coordinate axes at points that lie on circle $C$.
(I) Find the equation of circle $C$.
(II) If circle $C$ intersects the line $x+y+m=0$ at points $A$ and $B$, and $\overrightarrow{OA} \perp \overrightarrow{OB}$, find the value of $m$.

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