
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  $n\in N$   $n\geq2$  and the set  $X$  with  $n+1$  elements. The ordered sequences  $(a_{1}, a_{2},\ldots,a_{n})$  and  $(b_{1},b_{2},\ldots b_{n})$  of distinct elements of  $X$  are said to be  $\textit{separated}$  if there exists  $i\neq j$  such that  $a_{i}=b_{j}$ . Determine the maximal number of ordered sequences of  $n$  elements from  $X$  such that any two of them are  $\textit{separated}$ .
Note: ordered means that, for example  $(1,2,3)\neq(2,3,1)$ .

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