
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
Alice, Bob, and Carol play a game in which each of them chooses a number. Alice now chooses her number uniformly at random from all numbers between $\frac{1}{4}$ to $\frac{3}{4}$, Bob from $\frac{1}{3}$ to $\frac{3}{4}$, and Carol wants to maximize her chance of winning. The winner is whose number is between the other two. What number should Carol choose for her best chance to win?
A) $\frac{5}{12}$ 
B) $\frac{2}{5}$ 
C) $\frac{1}{2}$ 
D) $\frac{7}{12}$

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