
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. At the table, there can be either \( p \) people or \( q \) people, where \( p \) and \( q \) are relatively prime. Into what minimum number of pieces (not necessarily equal) should the pie be cut in advance so that it can be evenly distributed in either case?

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