
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
Let \( n \) be a given positive integer. A restaurant offers a choice of \( n \) starters, \( n \) main dishes, \( n \) desserts, and \( n \) wines. A merry company dines at the restaurant, with each guest choosing a starter, a main dish, a dessert, and a wine. No two people place exactly the same order. It turns out that there is no collection of \( n \) guests such that their orders coincide in three of these aspects, but in the fourth one they all differ. What is the maximal number of guests?

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