
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
On a 10 by 10 grid, 10 cells are marked. What is the largest value of $n$ such that, regardless of which cells are marked, it is always possible to find a rectangle consisting of several cells whose perimeter is at least $n$? The length or width of the rectangle can be one cell.

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