
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
A triangle $PQR$ is inscribed in the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Point $Q$ is at $(0,b)$, and $\overline{PR}$ is parallel to the $x$-axis. Foci $F_1$ and $F_2$ of the ellipse are on the $x$-axis at $(-c, 0)$ and $(c, 0)$ respectively, where $c = \frac{3}{5}a$. Assuming $F_1F_2 = 0.6a$, find $\frac{PQ}{PR}$.

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