
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
Joe now randomly chooses with equal probabilities either an apple, an orange, a banana, a pear, or a grape to eat for each of his three meals a day, and this goes on for two consecutive days. What is the probability that over these two days, Joe will eat at least two different kinds of fruit?

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