
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
Calculate how many squares, all sides parallel to the axes, can be formed within a region bounded by the equations \(y = 2x\), \(y = 0\), and \(x = 6\), where all vertices are integer coordinates.
- **A)** 48
- **B)** 51
- **C)** 55
- **D)** 57
- **E)** 60

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