
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 functions $f(x) = \left(\frac{1}{2}\right)^x$ and $g(x) = mx - 1$ ($m > 0$), if for every $x_1 \in [-1,2]$, there exists an $x_2 \in [-1,2]$ such that $f(x_1) = g(x_2)$, then the range of values for the real number $m$ is ______.

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