
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 a positive integer  $k$ , define the sequence  $\{a_n\}_{n\ge 0}$  such that  $a_0=1$  and for all positive integers  $n$ ,  $a_n$  is the smallest positive integer greater than  $a_{n-1}$  for which  $a_n\equiv ka_{n-1}\pmod {2017}$ . What is the number of positive integers  $1\le k\le 2016$  for which  $a_{2016}=1+\binom{2017}{2}?$ *Proposed by James Lin*

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