
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
Let $F_{1}$ and $F_{2}$ be the two foci of the ellipse $\dfrac{x^{2}}{4}+y^{2}=1$. Point $P$ lies on the ellipse. If the midpoint of segment $PF_{1}$ lies on the $y$-axis, determine the value of $\dfrac{|PF_{2}|}{|PF_{1}|}$.

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