
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
Define the set $H$ as consisting of points $(x,y)$ with integer coordinates where $2\le|x|\le6$ and $2\le|y|\le6$. How many squares with side length at least $4$ can have all their four vertices in $H$?
**A)** 4
    **B)** 8
    **C)** 12
    **D)** 16
    **E)** 20

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