
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
Four points $a$, $b$, $c$, and $d$ are chosen independently and at random from the interval $[0, m]$ for some positive integer $m$. Determine the smallest value of $m$ such that the probability of no three of $a$, $b$, $c$, and $d$ being within 0.5 units of each other exceeds $\frac{2}{3}$.
A) 10
B) 11
C) 12
D) 13
E) 14

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