
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 that line $l$ passes through point $M(-3,-3)$, and the distance from the center of the circle ${x}^{2}+{y}^{2}+4y-2=0$ to $l$ is $\sqrt{5}$.

(1) Find the length of the chord intercepted by the circle on line $l$;

(2) Find the equation of line $l$.

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