
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 certain task is completed in 12 days when workers A, B, and C work together. The same task would be completed in 15 days by workers A, B, and D; in 18 days by workers A, C, and D; and in 20 days by workers B, C, and D. How long will it take to complete the task if all four workers work together, but
a) A is absent on the first day?
b) C is absent on the last day?

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