
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
Given a natural number \( n > 1 \). Which is larger: the number of ways to cut a \( 3n \times 3n \) grid square into \( 1 \times 3 \) grid rectangles or the number of ways to cut a \( 2n \times 2n \) grid square into \( 1 \times 2 \) grid rectangles?

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