
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 the chord of the circle $x^{2}+y^{2}+4y-21=0$ passing through the point $P(-3,-3)$ has a length of $8$. Find:<br/>
$(1)$ the distance from the center of the circle to the line $l$;<br/>
$(2)$ the equation of the line $l$.

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