
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
How many natural numbers  $n$  satisfy the following conditions:
 i)  $219<=n<=2019$ ,
 ii) there exist integers  $x, y$ , so that  $1<=x<n<y$ , and  $y$  is divisible by all natural numbers from  $1$  to  $n$  with the exception of the numbers  $x$  and  $x + 1$  with which  $y$  is not divisible by.

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