
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 $x+y-1=0$, and its center is in the second quadrant with a radius of $\sqrt{2}$.
(1) Find the equation of circle C;
(2) Find the length of the chord cut by the line $2x+4y-1=0$ on circle C.

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