
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
4. k pieces are placed in k squares of an n x n (n ≥ 2) grid (with exactly one piece in each square), and in each 2 x 2 subgrid, there are exactly two pieces. Find all possible values of k.
(The 62nd Belarusian Mathematical Olympiad)

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