
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 the left and right foci of ellipse $\text{E}$ are ${F}_{1}$ and ${F}_{2}$, a line passing through ${F}_{1}$ with a slope of $2$ intersects ellipse $\text{E}$ at points $R$ and $Q$. If triangle $P{F}_{1}{F}_{2}$ is a right triangle, find the eccentricity of ellipse $\text{E}$.

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