
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 that satisfy \( 0 \leq x \leq 3, 0 \leq y \leq 2, \) and \( 0 \leq z \leq 5 \). Two distinct points are randomly chosen from \( T \). What is the probability that the midpoint of the segment they determine also belongs to \( T \)?

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