
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 $XYZ$, $XY = 4$, $XZ = 6$, and $YZ = 5$. The medians $XM$, $YN$, and $ZO$ of triangle $XYZ$ intersect at the centroid $T$. Let the projections of $T$ onto $YZ$, $XZ$, and $XY$ be $U$, $V$, and $W$, respectively. Find $TU + TV + TW$.

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