
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
Each box in the new grid diagram forms part of a larger layout composed of squares. Determine the total number of different-sized squares that can be traced using the lines in this expanded grid:

[asy]
unitsize(0.2 inch);
for (int i=0; i <= 6; ++i) {
  draw((i,0)--(i,6));
}
for (int j=0; j <= 6; ++j) {
  draw((0,j)--(6,j));
}
[/asy]

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