
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
To guard a certain target, someone needs to be on duty day and night, thus there are day shifts and night shifts. A guard can be scheduled for a single day shift, or a single night shift, or a continuous 24-hour shift. After completing a day shift, a night shift, or a 24-hour shift, the guard must rest for at least 1 day, 1.5 days, or 2.5 days respectively. If each shift requires 1 person, what is the minimum number of people needed to participate in the duty rotation?

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