
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 $$C_{1}: x^{2}+y^{2}-4x-2y-5=0$$ and $$C_{2}: x^{2}+y^{2}-6x-y-9=0$$.
(1) Find the equation of the line where the common chord of the two circles lies.
(2) A line $\iota$ passes through the point (4, -4) and intersects circle $C_{1}$ at points A and B, with $$|AB|=2 \sqrt {6}$$. Find the equation of line $\iota$.

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