
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) = sin2x + 2√3cos²x - √3, and the function g(x) = mcos(2x - π/6) - 2m + 3 (m > 0), if there exist x₁, x₂ ∈ [0, π/4] such that f(x₁) = g(x₂) holds true, then the range of the real number m is _______.

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