
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
Arrange a performance sequence consisting of 5 singing programs and 4 dance programs with the following requirements:
(1) How many different arrangements are there such that no two dance programs are adjacent to each other?
(2) How many different arrangements are there if singing programs and dance programs are to be arranged in alternating order?

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