
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 can be formed on a 3x3 grid where each side of the grid is 2 units apart and diagonal connections are allowed only between directly adjacent points? [asy]
size(70);
for (int i=0; i<=2; ++i) {
    for (int j=0; j<=2; ++j) {
        dot((10*i,10*j));
        if (i < 2) {
            draw((10*i, 10*j)--(10*(i+1), 10*j));
            draw((10*i, 10*j)--(10*i, 10*(j+1)));
        }
        if (j < 2) {
            draw((10*i, 10*j)--(10*(i+1), 10*(j+1)));
        }
    }
}
[/asy]

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