
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
Let  $P(x)$  be the product of all linear polynomials  $ax+b$ , where  $a,b\in \{0,\ldots,2016\}$  and  $(a,b)\neq (0,0)$ . Let  $R(x)$  be the remainder when  $P(x)$  is divided by  $x^5-1$ . Determine the remainder when  $R(5)$  is divided by  $2017$ .

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