
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
Given that the range of the function $f(x)$ is $[0,4]$ where $x\in [-2,2]$, and the function $g(x)=ax-1$ where $x\in [-2,2]$. For any $x_1\in [-2,2]$, there always exists $x_0\in [-2,2]$ such that $g(x_0)=f(x_1)$. Determine the range of the real number $a$.

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