
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
By decomposing a square, we mean dividing it into a finite number of rectangles whose sides are parallel to the sides of the square. A decomposition is called primitive if it is not a division of a larger decomposition. For which $n$ does a primitive decomposition of a square into $n$ rectangles exist?

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