
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 project can be completed by person A alone in 30 days, by person B alone in 60 days, and by person C alone in 40 days. If the three work together, with A resting for one day after every two days of work, B resting for one day after every three days of work, and C resting for one day after every five days of work, how many days will it take to complete the project?

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