
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
In the Cartesian coordinate plane $(xOy)$, the chord length intercepted by the line $x-y+1=0$ on the circle with the origin $O$ as the center is $\sqrt{6}$.

(1) Find the equation of circle $O$;

(2) If line $l$ is tangent to circle $O$ in the first quadrant and intersects the coordinate axes at points $D, E$, find the equation of line $l$ when the length of $DE$ is minimum.

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