
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 xOy, the curve $y = x^2 - 2x - 3$ intersects the coordinate axes at points lying on circle C.

1. Find the equation of circle C.
2. If the line $x + y + a = 0$ intersects circle C at points A and B, and $AB = 2$, find the value of $a$.

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