
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
The probability that event $A$ occurs is $\frac{5}{6}$; the probability that event $B$ occurs is $\frac{3}{4}$. Let $p$ be the probability that both $A$ and $B$ occur. Find the smallest interval that necessarily contains $p$.
A) $\Big[0, \frac{2}{3}\Big]$
B) $\Big[0, \frac{3}{4}\Big]$
C) $\Big[\frac{1}{12}, \frac{3}{4}\Big]$
D) $\Big[\frac{1}{12}, \frac{5}{6}\Big]$
E) $\Big[0, \frac{5}{6}\Big]$

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