
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
According to the definition of acute angle trigonometric functions, we know that for any acute angle $\alpha$, it holds that $\sin^2\alpha + \cos^2\alpha = 1$. If the equation $3x^2\sin\alpha - 4x\cos\alpha + 2 = 0$ has real roots, then the range of values for the acute angle $\alpha$ is.

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