
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) Find the standard equation of the hyperbola with foci on the x-axis, $c= \sqrt {6}$, and passing through the point $(-5, 2)$.
(2) Given two points on the hyperbola, $P_1(3, -4 \sqrt {2})$ and $P_2(\frac {9}{4}, 5)$, find the standard equation of the hyperbola.

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