
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 two circles $C_{1}$: $(x^{2} + y^{2} + 2x + 8y - 8 = 0)$ and $C_{2}$: $(x^{2} + y^{2} - 4x - 4y - 2 = 0)$
1. Find the equations of the lines containing the common chords of the two circles;
2. Find the length of the common chords of the two circles.
3. Line $l$ passes through the point $(3,-1)$ and intersects with circle $C_{1}$ at points $A$ and $B$, with $|AB|=6$. Find the equation of line $l$.

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