
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) = x^2 - 4x + 3 and g(x) = mx + 3 - 2m, if for any x1 in the interval [0, 4], there always exists an x2 in the interval [0, 4] such that f(x1) = g(x2), find the range of values for the real number m.

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