
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
At breakfast, lunch, and dinner, Joe randomly chooses either an apple, an orange, a banana, or a grape to eat. The probabilities are 0.4 for an apple, 0.3 for an orange, 0.2 for a banana, and 0.1 for a grape. What is the probability that Joe will eat at least two different kinds of fruit on a given day?

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