
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 chef has ten assistants, some of whom are friends with each other. Each working day, the chef appoints one or more assistants on duty, and each of the assistants on duty takes one cake for each of their non-duty friends at the end of the day. In the end, the chef learns the number of cakes that went missing. Will the chef be able to determine who of the assistants are friends with each other in 45 working days?

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