
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 line $l: y = x + m$ and the circle $C: x^2 + y^2 - 2x + 4y - 4 = 0$ intersect at two distinct points $A$ and $B$.
1. Find the range of values for $m$.
2. If the circle with diameter $AB$ passes through the origin, find the equation of line $l$.

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