
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 the function $g\left(x\right)=ax+2\left(a \gt 0\right)$ and $f\left(x\right)=x^{2}+2x$, for $\forall x_{1}\in \left[-1,1\right]$, $\exists x_{0}\in \left[-2,1\right]$ such that $g(x_{1})=f(x_{0})$ holds, then the range of $a$ is ______.

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