
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 community concert attended by five students, including A and B, each student's performance is arranged to be performed consecutively. If a lottery method is used to randomly determine the order of performances (numbered 1, 2, 3, 4, 5):  
(1) The probability that at least one of the performance numbers of A and B is even;  
(2) The probability that the performance numbers of A and B are not adjacent.

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