
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 in the Cartesian plane with coordinates \( (x, y) \) that satisfy the following conditions:
1. \( b \leq x \leq 3b \)
2. \( b \leq y \leq 3b \)
3. \( x + y \geq 2b \)
4. \( x + 2b \geq y \)
5. \( y + 2b \geq x \)

The boundary of the set \( T \) 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}
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