
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
Segments $AD=12$, $BE=8$, and $CF=30$ are drawn from the vertices of triangle $ABC$, each perpendicular to a straight line $RS$, which does not intersect the triangle. Points $D$, $E$, and $F$ are the intersection points of $RS$ with the perpendiculars. If $x$ represents the length of the perpendicular segment $GH$ drawn to $RS$ from the intersection point $G$ of the medians of the triangle, find $x$.
A) $\frac{16}{3}$
B) $\frac{40}{3}$
C) $\frac{50}{3}$
D) $\frac{80}{3}$
E) $\frac{100}{3}$

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