
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 that passes through the point A(0, 3) and whose center lies on the negative half of the y-axis, with a radius of 5.
(1) Find the standard equation of circle C.
(2) If the chord intercepted by line l passing through point M(-3, -3) has a length of $4\sqrt{5}$, find the equation of line l.

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