
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
Consider two events, $C$ and $D$, with the (conditional) probability that event $C$ occurs being $\frac{5}{6}$ and the probability that event $D$ occurs given that $C$ has occurred is $\frac{3}{5}$. Determine the smallest interval necessarily containing the probability $q$ that both $C$ and $D$ occur.
**A)** $[0, \frac{1}{2}]$   
**B)** $[\frac{1}{2}, \frac{5}{6}]$  
**C)** $[\frac{1}{2}, 1]$  
**D)** $[\frac{3}{5}, \frac{5}{6}]$  
**E)** $[\frac{5}{6}, 1]$

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