
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
Consider a $10 \times 10$ grid, consisting of 100 squares. The rows of the grid are numbered from top to bottom in order from 1 to 10: the highest row is number 1, the lowest is number 10. The columns of the grid are numbered from left to right in order from 1 to 10: the leftmost column is number 1, the rightmost is number 10. Martin colors some of the squares of the grid, such that for any colored square $c$, there is at most one other colored square different from $c$ whose column number is greater than or equal to that of $c$ and whose row number is greater than or equal to that of $c$.

What is the maximum number of squares that Martin can color?

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