
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
Consider all possible sets of natural numbers  $(x_1, x_2, ..., x_{100})$  such that  $1\leq x_i \leq 2017$  for every  $i = 1,2, ..., 100$ . We say that the set  $(y_1, y_2, ..., y_{100})$  is greater than the set  $(z_1, z_2, ..., z_{100})$  if  $y_i> z_i$  for every  $i = 1,2, ..., 100$ . What is the largest number of sets that can be written on the board, so that any set is not more than the other set?

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