
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 the points in the square \(\{(x ; y):-\pi \leq x \leq 2 \pi, 0 \leq y \leq 3 \pi\}\) satisfy the system of equations:
\[
\left\{\begin{array}{l}
\sin x+\sin y=\sin 3 \\
\cos x+\cos y=\cos 3
\end{array}\right.
\]
Find the coordinates \((x ; y)\) of all such points.

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