
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 \(\theta \in[0,2 \pi]\) and for \(x \in [0,1]\), the function
\[ f(x) = 2x^2 \sin \theta - 4x(1-x) \cos \theta + 3(1-x)^2 > 0, \]
determine the range of values for \(\theta\).

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