
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 $S' = \{(x, y, z) |\ x, y, z \in \mathbb{Z}, 0 \le x \le 3, 0 \le y \le 4, 0 \le z \le 5\}$. Two distinct points are randomly chosen from $S'$. The probability that the midpoint of the segment they determine also belongs to $S'$, provided that at least one coordinate of each point must be even, 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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