
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 C with the equation $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ ($a, b > 0$), where the focal length is 10, and the point P(3, 4) lies on one of the asymptotes of C, determine the standard equation of hyperbola C.

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