
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
An integer  $n\ge1$  is *good* if the following property is satisfied:
If a positive integer is divisible by each of the nine numbers  $n + 1, n + 2, ..., n + 9$ , this is also divisible by  $n + 10$ .
How many good integers are  $n\ge 1$ ?

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