
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 $H$ by the points $(x,y)$ with integer coordinates, where $1\le|x|\le7$, and $1\le|y|\le7$. How many squares with a side length of at least $5$ can be formed such that all their vertices belong to $H$?

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