
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 circle \( C_1: x^2 + y^2 - a = 0 \) is symmetric about the line \( l \). The resulting circle is \( C_2: x^2 + y^2 + 2x - 2ay + 3 = 0 \). Find the equation of the line \( l \).

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