
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 an ellipse E with its left and right foci as F_1 and F_2 respectively, a line passing through F_1 with a slope of 2 intersects the ellipse E at points P and Q. If ∆PF_1F_2 is a right-angled triangle, and |PF_1| < |F_1F_2|, calculate the eccentricity of the ellipse E.

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