
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
The value of $\theta$ such that the distance from the point $(\cos \theta, \sin \theta)$ to the line $x\sin \theta + y\cos \theta - 1 = 0$ is $\frac{1}{2}$, where $0 \leq \theta \leq \frac{\pi}{2}$, is $\theta = \boxed{\frac{\pi}{12}}, \boxed{\frac{5\pi}{12}}$, or is $\boxed{\frac{\pi}{12}}$ or $\boxed{\frac{5\pi}{12}}$.

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