
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
Suppose that \(x\) and \(y\) satisfy the equations
\[
\begin{aligned}
& 3 \sin x + 4 \cos y = 5 \\
& 4 \sin y + 3 \cos x = 2
\end{aligned}
\]

What is the value of \(\sin (x + y)\)?

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