
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  $p=2017$  be a prime.  Find the remainder when \[\left\lfloor\dfrac{1^p}p\right\rfloor + \left\lfloor\dfrac{2^p}p\right\rfloor+\left\lfloor\dfrac{3^p}p\right\rfloor+\cdots+\left\lfloor\dfrac{2015^p}p\right\rfloor \] is divided by  $p$ .  Here  $\lfloor\cdot\rfloor$  denotes the greatest integer function.

*Proposed by David Altizio*

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