
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
The line RS does not intersect with △ABC. Perpendiculars are drawn from the vertices A, B, and C of △ABC to line RS, and the corresponding feet of the perpendiculars are D, E, and F respectively. It is given that AD = 10, BE = 6, and CF = 24. Let H be the foot of the perpendicular drawn from the centroid G of △ABC to line RS. If x denotes the length of the segment GH, find x.

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