
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 $XYZ$, points $M$, $N$, and $O$ are located on sides $\overline{YZ},$ $\overline{XZ},$ and $\overline{XY},$ respectively, such that $YM: MZ = ZN:NX = XO:OY = 2:3$. Let $G$, $H$, and $I$ be the intersections of the line segments $\overline{XM},$ $\overline{YN},$ and $\overline{ZO}$ respectively. Compute the ratio $\frac{[GHI]}{[XYZ]}$.

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