
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 $n \geq 1$ be an integer. You have $n$ cubes with side lengths $1, 2, \dots, n$. You want to stack them in a certain order such that a cube with side length $k$ can only be placed on a cube with side length $\ell$ with $\ell \geq k-2$. How many different such stackings exist?

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