
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 that \(a\) and \(b\) are nonzero constants, and the variable \(\theta\) satisfies the system of inequalities:

\[
\left\{
\begin{array}{l}
a \sin \theta + b \cos \theta \geq 0 \\
a \cos \theta - b \sin \theta \geq 0
\end{array}
\right.
\]

find the maximum value of \(\sin \theta\).

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