
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 $\theta,$ where $0 \leq \theta \leq 2\pi,$ so that for all $x$ in the interval [0,1],
\[
x^2 \cos \theta - kx(1-x) + (1-x)^2 \sin \theta > 0,
\]
where $k$ is a positive constant. Determine the values for $\theta$ when $k=3$.

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