
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
Given that medians $DR$ from $D$ to $EF$ and $ES$ from $E$ to $DF$ intersect at centroid $G$, and line $RT$ meets $ES$ at $H$, let $T$ be the midpoint of $DF$, find the area of triangle $DEF$ in terms of the area of triangle $RGH$.

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