
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
Given that the probability event $A$ occurs is $\frac{5}{6}$, and the probability event $B$ occurs is $\frac{1}{2}$, what is the smallest interval that necessarily contains the probability $p$ that both $A$ and $B$ occur?
**A)** $\left[0, \frac{1}{2}\right]$
**B)** $\left[\frac{1}{4}, \frac{3}{4}\right]$
**C)** $\left[\frac{1}{3}, \frac{1}{2}\right]$
**D)** $\left[\frac{5}{6}, 1\right]$
**E)** $\left[\frac{1}{6}, \frac{1}{2}\right]$

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