
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
Write the standard equation of a hyperbola that meets the following conditions:
(1) $a=3$, $b=4$ with foci on the x-axis;
(2) Foci at $(0,5)$, $(0,-5)$ and passing through point $\left(2, \dfrac {3 \sqrt {5}}{2}\right)$.

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