
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 $x$, $y$, $z$, and $w$ are chosen independently and at random from the interval $[0,m]$ for some positive integer $m$. Find the smallest possible value of $m$ such that the probability that no two of $x$, $y$, $z$, and $w$ are within 0.5 unit of each other is greater than $\frac{3}{4}$.
A) 15
B) 16
C) 17
D) 18
E) 19

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