
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
Three machines perform certain work. If the first machine works alone, it will finish the work $a$ days later than if all machines worked together. If the second machine works alone, it will finish $b$ days later than if all worked together. If the third machine works alone, it will take $c$ times longer than if all worked together. How many days does each machine work individually? What values can $c$ take?

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