
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
Let $T$ be the set of points whose coordinates $x,$ $y,$ and $z$ are integers satisfying $0\le x\le3,$ $0\le y\le4,$ and $0\le z\le5.$ Two distinct points are randomly chosen from $T.$ The probability that the midpoint of the segment they determine also belongs to $T$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$

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