
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
In a biology laboratory of a certain school, there is an aquarium containing 6 fish, among which 4 are black and 2 are red. A biology teacher has classes 4 days a week, with one class in the morning and one in the afternoon. Before each class, the teacher randomly selects one fish from the aquarium for use and returns it to the aquarium after use.  
(1) Calculate the probability that the fish caught by the biology teacher in the morning and afternoon of the same day are of the same color;  
(2) Calculate the probability that the teacher catches fish of different colors in the morning and afternoon sessions on exactly two days of the week.

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