
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
If F_1 and F_2 are the left and right foci of the ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ (a > b > 0) respectively, and the midpoint of the line segment PF_1 is on the y-axis, find the eccentricity of the ellipse given that ∠PF_1F_2=30^{\circ}.

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