
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. (For example, there are no  $n$  people that order exactly the same three courses of food, but  $n$  different wines.) What is the maximal number of guests?

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