
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 rectangles are there whose four vertices are points on a larger grid, given by the points (0,0), (0,5), (0,10), (0,15), (5,0), (5,5), (5,10), (5,15), (10,0), (10,5), (10,10), (10,15), (15,0), (15,5), (15,10), (15,15)?

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