
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
(1) Given the circles C<sub>1</sub>: $x^2 + y^2 + 2x + 8y - 8 = 0$ and C<sub>2</sub>: $x^2 + y^2 - 4x - 4y - 2 = 0$, determine the relationship between circle C<sub>1</sub> and circle C<sub>2</sub>.

(2) Given a line l passing through the point M(-3,-3) that intersects the circle $x^2 + y^2 + 4y - 21 = 0$ to form a chord with length $4\sqrt{5}$, find the equation of line l.

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