
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 equation x^2/a^2 - y^2/b^2 = 1 where a > 0 and b > 0, and its two focal points are F1 and F2. Point A(√3,1) lies on C and satisfies the condition that the dot product of vectors AF1 and AF2 is 0. Determine the eccentricity of the hyperbola C.

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