
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 the function $y=f(x)$ be defined on $\mathbb{R}$ with a period of 1. If $g(x)=f(x)-2x$ has a range of $[-2,6]$ on the interval $[2,3]$, then determine the range of the function $g(x)$ on the interval $[-12,12]$.

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