
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
Let $a$ be a positive number. Consider the set $S$ of all points whose rectangular coordinates $(x, y)$ satisfy all of the following conditions:
$\text{(i) }\frac{a}{2}\le x\le 2a\qquad \text{(ii) }\frac{a}{2}\le y\le 2a\qquad \text{(iii) }x+y\ge 3a\qquad \text{(iv) }x+a\ge y\qquad \text{(v) }y+a\ge x$
The boundary of set $S$ is a polygon with how many sides?
**A)** 3 sides  
**B)** 4 sides  
**C)** 5 sides  
**D)** 6 sides  
**E)** 7 sides

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