
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 $XYZ,$ point $E$ lies on $\overline{XZ}$ and point $G$ lies on $\overline{XY}.$ Let $\overline{XE}$ and $\overline{YG}$ intersect at $Q.$

If $XQ:QE = 3:2$ and $GQ:QY = 3:1,$ find $\frac{XG}{GY}.$

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