
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 the ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1 \left( a > b > 0 \right)$ intersects with the negative half of the $x$-axis at point $A$, $P$ is a point on the ellipse in the first quadrant, the line $OP$ intersects the ellipse at another point $Q$, the left focus of the ellipse is $F$, if the line $PF$ bisects segment $AQ$, then the eccentricity of the ellipse is __________.

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