
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
Integer sequence  $(x_{n})$  is defined as follows;  $x_{1} = 1$ , and for each integer  $n \geq 1$ ,  $x_{n+1}$  is equal to the largest number that can be obtained by permutation of the digits of  $x_{n}+2$ . Find the smallest  $n$  for which the decimal representation of  $x_{n}$  contains exactly  $2022$  digits

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