
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 $AD=14$, $BE=10$, and $CF=28$ are drawn from the vertices of triangle $ABC$, each perpendicular to a straight line $RS$, not intersecting the triangle. Points $D$, $E$, and $F$ are where these perpendiculars intersect line $RS$. A segment $GH$ is drawn perpendicular from the intersection point $G$ of the medians of triangle $ABC$ to line $RS$. Calculate the length $x$ of segment $GH$.
A) $\frac{48}{3}$  
B) $\frac{52}{3}$  
C) $\frac{54}{3}$  
D) $\frac{58}{3}$

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