
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
In triangle $XYZ$, $G$, $H$, and $I$ are points on the sides $\overline{YZ},$ $\overline{ZX},$ and $\overline{XY},$ respectively, such that the ratios $YG:GZ$, $ZH:HX$, and $XI:IY$ are $2:3$. Triangle $XYZ$ is divided by line segments $\overline{XG}$, $\overline{YH}$, and $\overline{ZI}$, which intersect at points $P, Q$, and $R$ respectively. Compute the ratio $\frac{[PQR]}{[XYZ]}$.

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