
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
We are given sufficiently many stones of the forms of a rectangle  $2\times 1$  and square  $1\times 1$ . Let  $n > 3$  be a natural number. In how many ways can one tile a rectangle  $3 \times n$  using these stones, so that no two  $2 \times 1$  rectangles have a common point, and each of them has the longer side parallel to the shorter side of the big rectangle?

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