
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 $DEF$, $DE = 4$, $DF = 6$, and $EF = 5$. The medians $DG$, $EH$, and $FI$ of triangle $DEF$ intersect at the centroid $J$. Let the projections of $J$ onto $EF$, $DF$, and $DE$ be $S$, $T$, and $U$, respectively. Find $JS + JT + JU$.

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