
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:
\(\text{(i) }b \leq x \leq 3b\)
\(\text{(ii) }b \leq y \leq 3b\)
\(\text{(iii) }x + y \geq 2b\)
\(\text{(iv) }x + 2b \geq 2y\)
\(\text{(v) }y + 2b \geq 2x\)
The boundary of set \( T \) is a polygon with how many sides?
A) 5 sides
B) 6 sides
C) 7 sides
D) 8 sides

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