
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
If the two foci of the hyperbola \(L\) are precisely the two vertices of the ellipse \(T: \frac{x^{2}}{16}+\frac{y^{2}}{9}=1\), and the two vertices of the hyperbola \(L\) are exactly the two foci of the ellipse \(T\), then find the equation of the hyperbola \(L\).

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