
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
It is known that the circle C: $x^2 + y^2 + Dx + Ey + 3 = 0$ is symmetric with respect to the line $x + y - 1 = 0$, has a radius of $\sqrt{2}$, and that the center of circle C is located in the second quadrant.
(Ⅰ) Find the equation of circle C.
(Ⅱ) Find the equation of the line l, not passing through the origin, whose intercepts on the x-axis and y-axis are equal, and that is tangent to circle C.

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