
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
In a $7 \times 7$ grid, several cells are marked such that there is at least one marked cell in each row and each column. It turns out that in any row of the grid, the number of marked cells is odd, and in any column, the number of marked cells is divisible by 3. What is the minimum and maximum number of cells that could be marked?

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