
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 coordinates $(x; y)$ of points in the square $\{(x; y) : -2\pi \leq x \leq 3\pi, -\pi \leq y \leq 4\pi \}$ satisfy the system of equations $\left\{
\begin{array}{l}
\sin x + \sin y = \sin 4 \\
\cos x + \cos y = \cos 4 
\end{array}
\right.$. How many such points are there? Find the coordinates $(x; y)$ of the points with the largest abscissa.

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