
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
The hyperbola C has the same focal length as the ellipse given by the equation $\frac{x^2}{9} + \frac{y^2}{4} = 1$, and one asymptote of the hyperbola is given by the equation x - 2y = 0. Determine the standard equation of the hyperbola C.

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