
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
Triangle $XYZ$ has $XY=15, YZ=18,$ and $XZ=21$. Let $Q$ be the point on $\overline{XZ}$ such that $ZQ=15$. Identify two points $F$ and $G$ on line $YQ$ such that quadrilaterals $XYFZ$ and $XYGZ$ are trapezoids. What is the distance $FG$?
A) 24
B) 30
C) 36
D) 42
E) 48

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