
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 $XYZ$, $XY=15, YZ=18$, and $XZ=21$. Let $Q$ be a point on $\overline{XZ}$ such that $QZ=12$. Exactly two points $F$ and $G$ sit on line $YQ$ such that quadrilaterals $XYFZ$ and $XYGZ$ are trapezoids. Determine the distance $FG$.
A) 4
B) 6
C) 8
D) 10

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