
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 \(a\), \(b\), and \(\theta\) satisfy the system of equations:

\[
\left\{
\begin{array}{l}
\sin \theta + \cos \theta = a \\
\sin \theta - \cos \theta = b \\
\sin^2 \theta - \cos^2 \theta - \sin \theta = -b^2
\end{array}
\right.
\]

find the values of \(a\) and \(b\).

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