
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 that the center of circle C lies on the line y = x + 1, with a radius of $\sqrt{2}$. The circle passes through points P(3, 6) and Q(5, 6).
1. Find the equation of circle C.
2. The chord formed by cutting the circle with a line l passing through point (3, 0) has a length of 2. Find the equation of line l.

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