
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
Which angles satisfy - between 0 and \(2 \pi\) - the following system of equations:

\[
\begin{aligned}
& \sin x+\cos y=0 \\
& \cos x \sin y=-\frac{1}{2} \\
\end{aligned}
\]

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