
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>, F<sub>2</sub> be the two foci of the hyperbola C: $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1$$ (s>0, b>0), and let P be a point on C. If |PF<sub>1</sub>|+|PF<sub>2</sub>|=4a, and the sine of the smallest internal angle of △PF<sub>1</sub>F<sub>2</sub> is $$\frac {1}{3}$$, then find the eccentricity of C.

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