
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
A set of  $n$  positive integers is said to be *balanced* if for each integer  $k$  with  $1 \leq k \leq n$ , the average of any  $k$  numbers in the set is an integer. Find the maximum possible sum of the elements of a balanced set, all of whose elements are less than or equal to  $2017$ .

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