
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
For each integer  $n\geq 1$ , let  $S_n$  be the set of integers  $k > n$  such that  $k$  divides  $30n-1$ .  How many elements of the set \[\mathcal{S} = \bigcup_{i\geq 1}S_i = S_1\cup S_2\cup S_3\cup\ldots\] are less than  $2016$ ?

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