
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 that the asymptotes of a hyperbola are $3x+4y=0$ and it passes through the point $(8,3 \sqrt {3})$, find the equation of the hyperbola;
(2) If the chord $MN$ of the hyperbola in (1) is bisected by the point $A(8,3)$, find the equation of the line containing $MN$.

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