
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 $F_{1}$ and $F_{2}$ are the left and right foci of the ellipse $C$: $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b > 0)$, and $Q$ is a point on the ellipse $C$ such that $\triangle QF_{1}O$ ($O$ is the origin) is an equilateral triangle. If the rays $QF_{1}$ and $QO$ intersect the ellipse at points $P$ and $R$ respectively, then the ratio of the areas of $\triangle QF_{1}O$ and $\triangle QPR$ is \_\_\_\_\_\_.

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