
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 two circles C and D: $(x-1)^2+(y+2)^2=4$ are symmetric about the line $y=x$.
(Ⅰ) Find the standard equation of circle C;
(Ⅱ) If the line $l: y=kx+1$ intersects circle C at points A and B, and $|AB|=2\sqrt{3}$, find the equation of line $l$.

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