
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 a circle $C$: $x^{2}+y^{2}+Dx+Ey+3=0$ is symmetric about the line $x+y-1=0$, has a radius of $\sqrt{2}$, and its center $C$ is in the second quadrant.
(Ⅰ) Find the equation of circle $C$;
(Ⅱ) A line $l$, which does not pass through the origin and has equal intercepts on the $x$-axis and $y$-axis, is tangent to circle $C$. Find the equation of line $l$.

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