
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
Real numbers $x$, $y$, and $z$ are selected independently from the interval $[0, m]$ for some positive integer $m$. The probability that no two of $x$, $y$, and $z$ are within 2 units of each other and the sum $x + y + z \geq m$ is greater than $\frac{3}{5}$. What is the smallest possible value of $m$?
A) 25
B) 27
C) 30
D) 32
E) 34

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