
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
Let F<sub>1</sub> and F<sub>2</sub> be the two foci of a hyperbola C: $$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$$ with a focal length of 6. Let P be a point on C. If |PF<sub>1</sub>| + |PF<sub>2</sub>| = 6a, and the smallest internal angle of triangle △PF<sub>1</sub>F<sub>2</sub> is 30°, then the equation of C is _______ .

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