
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
A, B, C, and D are four typists undertaking a typing task. If the task is to be completed by any one of them alone, A would need 24 hours, B would need 20 hours, C would need 16 hours, and D would need 12 hours.
(1) If A, B, C, and D type at the same time, how much time is needed to complete the task?
(2) If they type in turns in the order of A, B, C, D, A, B, C, D... with each person typing for one hour in each round, how much time is needed to complete the task?
(3) Is it possible to adjust the order of A, B, C, D mentioned in (2) without changing anything else, so that the time to complete the typing task is reduced by at least half an hour? If yes, please provide a rotation order; if no, please explain why.

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