
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 points F1 and F2 are the left and right foci of the ellipse $$\frac {x^{2}}{a^{2}}$$ + $$\frac {y^{2}}{b^{2}}$$ = 1 (a > b > 0), and P is a moving point on the ellipse. The point Q is on the extension of ray F1P and |$$\overrightarrow {PQ}$$| = |$$\overrightarrow {PF_{2}}$$|. If the minimum value of |$$\overrightarrow {PQ}$$| is 1 and the maximum value is 9, determine the eccentricity of the ellipse.

A) $$\frac {3}{5}$$
B) $$\frac {1}{3}$$
C) $$\frac {4}{5}$$
D) $$\frac {1}{9}$$

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