
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
Find all possible  $\{ x_1,x_2,...x_n \}$  permutations of  $ \{1,2,...,n \}$  so that  when  $1\le i \le n-2 $  then we have   $x_i < x_{i+2}$  and when  $1 \le i \le n-3$  then we have   $x_i < x_{i+3}$  . Here  $n \ge 4$ .

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