
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 $b$ be a positive number. Consider the set $T$ of all points whose rectangular coordinates $(x, y)$ satisfy all of the following conditions:
$\text{(i) }b\le x\le 4b\qquad \text{(ii) }b\le y\le 4b\qquad \text{(iii) }x+y\ge 3b$
$\text{(iv) }x+2b\ge 2y\qquad \text{(v) }2y\ge x+b$
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