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

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