
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 circle C: x² + y² + 2x - 4y + 3 = 0

1. Find the equation of the line l that is tangent to the circle C, does not pass through the origin, and has equal intercepts on the x-axis and y-axis.
2. Find the equation of the line passing through the origin and intercepted by the circle C with a segment length of 2.

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