
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 $\frac{x^{2}}{16} + \frac{y^{2}}{12} = 1$ with left focus $F_{1}$ and right focus $F_{2}$. Point $P$ lies on the ellipse. If the midpoint of segment $PF_{1}$ is on the $y$-axis, then $|PF_{1}| : |PF_{2}| =$\_\_\_\_\_\_\_\_\_\_.

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