
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
Determine all angles \(\theta,\) \(0 \leq \theta \leq 2\pi,\) such that for all real numbers \(x,\) \(0 \leq x \leq 2,\)
\[ x^2 \sin \theta - x(2 - x) + (2 - x)^2 \cos \theta > 0. \]

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