
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
Let the probability that event $A$ occurs be $\frac{4}{5}$, the probability that event $B$ occurs be $\frac{3}{4}$, and the probability that event $C$ occurs be $\frac{2}{3}$. Find the smallest interval necessarily containing the probability that all three events $A$, $B$, and $C$ occur.

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