For two constants $a$ ($1 \leq a \leq 2$) and $b$, the function $f(x) = \sin(ax + b + \sin x)$ satisfies the following conditions. (가) $f(0) = 0$ and $f(2\pi) = 2\pi a + b$ (나) The minimum positive value of $t$ such that $f'(0) = f'(t)$ is $4\pi$. Let $A$ be the set of all values of $\alpha$ in the open interval $(0, 4\pi)$ where the function $f(x)$ has a local maximum. If $n$ is the number of elements in set $A$ and $\alpha_{1}$ is the smallest element in set $A$, then $n\alpha_{1} - ab = \frac{q}{p}\pi$. What is the value of $p + q$? [4 points]

2) For the bicycle to proceed smoothly on the platform it is necessary that: – to the left and right of the points of non-differentiability the sections of the graph are orthogonal; – the length of the side of the square wheel equals the length of a "bump", that is, the arc of the curve with equation $y = f(x)$ for $x \in [-a; a]$.
Establish whether these conditions are satisfied.${ } ^ { 1 }$