
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 $\theta \in [0, 2\pi]$, if for any $x \in [0, 1]$, the inequality $2x^{2} \sin \theta - 4x(1-x) \cos \theta + 3(1-x)^{2} > 0$ always holds, determine the range of values for $\theta$.

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