
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 within the square \(\{(x ; y):-\pi \leq x \leq \pi, 0 \leq y \leq 2 \pi\}\) satisfy the system of equations \(\left\{\begin{array}{c}\sin x + \sin y = \sin 2 \\ \cos x + \cos y = \cos 2\end{array}\right.\). How many such points are in the square? Find the coordinates \((x ; y)\) of the point with the smallest ordinate.

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