
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 $f(x) = x^2 - 2x$ and $g(x) = ax + 2$ where $a > 0$. For every $x_1 \in [-1, 2]$, there exists an $x_0 \in [-1, 2]$ such that $g(x_1) = f(x_0)$. Find the range of values for $a$.

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