
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 $y=f(x)$ be a function defined on $\mathbb{R}$ with a period of $1$. If $g(x) = f(x) - 2x$ has a range of $[-2, 6]$ on the interval $[2, 3]$, find the range of $g(x)$ on $[-2017, 2017]$.

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