
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:
$\text{(i) } b \leq x \leq 3b, \qquad \text{(ii) } b \leq y \leq 3b, \qquad \text{(iii) } x + y \geq 2b,\\ \\ \text{(iv) } x + 2b \geq 2y,\qquad \text{(v) } y + 2b \geq 2x$
A) 4 sides
B) 5 sides
C) 6 sides
D) 7 sides
E) 8 sides

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