
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 $\mathrm{P}$ be a point on the side $\mathrm{BC}$ of a triangle $\mathrm{ABC}$. The parallel through $\mathrm{P}$ to $\mathrm{AB}$ intersects side $\mathrm{AC}$ at point $\mathrm{Q}$, and the parallel through $\mathrm{P}$ to $\mathrm{AC}$ intersects side $\mathrm{AB}$ at point $\mathrm{R}$. The ratio of the areas of triangles $\mathrm{RBP}$ and $\mathrm{QPC}$ is $\mathrm{k}^{2}$.

Determine the ratio of the areas of triangles $\mathrm{ARQ}$ and $\mathrm{ABC}$.

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