
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
Let \( n \geq 2 \) be an integer. A sieve is an \( n \times n \) grid from which \( n \) cells have been removed, with exactly one removed in each row and column. A stick is a \( 1 \times k \) or \( k \times 1 \) rectangle of cells, where \( k \) is a strictly positive integer. For a sieve \( A \), let \( m(A) \) be the minimum number of sticks needed to partition \( A \). Determine the possible values of \( m(A) \).

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