
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 a hyperbola sharing the same foci with the hyperbola $\dfrac{x^{2}}{16}- \dfrac{y^{2}}{9}=1$ and passing through point $P\left(- \dfrac{ \sqrt{5}}{2},- \sqrt{6} \right)$, find the standard equation of this hyperbola.

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