
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 F_1 and F_2 are the left and right foci of the hyperbola C: $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ (a > 0, b > 0), O is the coordinate origin, and point P is on the right branch of hyperbola C with |F_1F_2| = 2|OP|. The area of △PF_1F_2 is a^2. Determine the eccentricity of hyperbola C.

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