
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
Robert returns to the bottling plant, now interested in both chocolate and vanilla milk. The plant bottles chocolate milk with a 3/4 chance and vanilla milk with a 1/2 chance each day. Robert plans to visit the plant for 6 days. What is the probability that the plant bottles chocolate milk exactly 4 times and vanilla milk at least 3 times in these 6 days?

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