
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
How many squares, each with sides parallel to the axes and vertices at integer coordinates, lie entirely within the region bounded by the triangle formed by \( y = 2x \), \( y = -2 \), and \( x = 5 \)?
**A**) 12  
**B**) 15  
**C**) 20  
**D**) 25  
**E**) 30

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