
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 system, the curve \( y=x^2-4x+3 \) intersects the coordinate axes at points lying on a circle \( C \).
(Ⅰ) Determine the equation of circle \( C \).
(Ⅱ) If circle \( C \) intersects the line \( x+y+m=0 \) at points \( A \) and \( B \), and \( \overrightarrow{OA} \) is perpendicular to \( \overrightarrow{OB} \), find the value of \( m \).

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