
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 $H$ be defined by the points $(x,y)$ where $(x,y)$ has integer coordinates such that $2 \leq |x| \leq 6$ and $2 \leq |y| \leq 6$. Determine the number of squares of side at least $4$ but less than or equal to $5$ whose four vertices lie in $H$.

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