
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 a line $l$ with a slope of $1$ passes through the right focus $F$ of the ellipse $\frac{x^{2}}{4}+y^{2}=1$ and intersects the ellipse at points $A$ and $B$, find the length of the chord $AB$.

(2) Find the equation of the hyperbola that shares the same asymptotes with the hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{16}=1$ and passes through the point $(-3,2\sqrt{3})$.

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