
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 sheet of graph paper of size $5 \times n$ is filled with cards of size $1 \times 2$ in such a way that each card entirely occupies two adjacent cells. Each card has the numbers 1 and -1 written on it. It is known that the products of the numbers by rows and columns of the resulting table are positive. For which values of $n$ is this possible?

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