
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 $f(x)=x^{2}-2x$ and $g(x)=ax+2$ $(a > 0)$, for all $x_{1} \in [-1,2]$, find the range of the real number $a$ such that for each $x_{1}$ in this interval, there exists $x_{0} \in [-1,2]$ such that $g(x_{1})=f(x_{0})$.

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