
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 $\frac{5}{7}$; the probability that event $B$ occurs is $\frac{4}{5}$. Assume events $A$ and $B$ are independent. Let $p$ be the probability that both $A$ and $B$ occur. Find the smallest interval necessarily containing $p$.
A) $\left[\frac{1}{5}, \frac{4}{7}\right]$
B) $\left[\frac{3}{7}, \frac{4}{5}\right]$
C) $\left[\frac{4}{7}, \frac{4}{7}\right]$
D) $\left[\frac{1}{7}, \frac{6}{7}\right]$
E) $\left[\frac{2}{7}, \frac{5}{7}\right]$

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