
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 the curve C: $x^2+y^2+2x+m=0$ ($m \in \mathbb{R}$)  
(1) If the trajectory of curve C is a circle, find the range of values for $m$;  
(2) If $m=-7$, and a line passing through point P(1, 1) intersects curve C at points A and B, with $|AB|=4$, find the equation of line AB.

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