
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
A grid consists of multiple squares, as shown below. Count the different squares possible using the lines in the grid.

[asy]
unitsize(0.5 cm);
int i, j;
for(i = 0; i <= 5; ++i) {
    draw((0,i)--(5,i));
    draw((i,0)--(i,5));
}
for(i = 1; i <= 4; ++i) {
    for (j = 1; j <= 4; ++j) {
        if ((i > 1 && i < 4) || (j > 1 && j < 4)) continue;
        draw((i,j)--(i,j+1)--(i+1,j+1)--(i+1,j)--cycle);
    }
}
[/asy]

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