
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
There are five students: A, B, C, D, and E;
(1) If these five students line up in a row, in how many ways can A not stand in the first position?
(2) If these five students line up in a row, and A and B must be next to each other while C and D must not be next to each other, in how many ways can they line up?
(3) If these five students participate in singing, dancing, chess, and drawing competitions, with at least one person in each competition, and each student must participate in exactly one competition, and A cannot participate in the dancing competition, how many participating arrangements are there?

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