
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 hostess baked a pie for guests. There can be either $p$ people or $q$ people at the table (where $p$ and $q$ are coprime). Into what minimal number of pieces (not necessarily equal) should the pie be cut in advance so that it can be distributed evenly in any case?

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