Let $u$ be a positive number. Consider the set $S$ of all points whose rectangular coordinates $(x, y)$ satisfy all of the following conditions:

1. $\frac{a}{2} \le x \le 2a$
2. $\frac{a}{2} \le y \le 2a$
3. $x + y \ge a$
4. $x + a \ge y$
5. $y + a \ge x$

The boundary of set $S$ is a polygon with how many sides?

Let's think step by step and output the final answer within \boxed{}.
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