
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 that the center of a hyperbola is at the origin of the Cartesian coordinate plane, the length of its real axis is 4, and one of its foci is F(0, 3), find the equation of the hyperbola.

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