
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
There are $n$ parking spaces along a road, and $n$ drivers each driving a car. Each driver parks their car in their preferred parking space. If their preferred space is already occupied, they park in the nearest available space along the road. If both their preferred and subsequent spaces are occupied, they drive away and do not park. How many sequences $\left(a_{1}, a_{2}, \cdots, a_{n}\right)$ exist such that every parking space is occupied? Here, $a_{i}$ represents the preferred parking space of the $i$-th driver, and the values of $a_{1}, a_{2}, \cdots, a_{n}$ do not need to be distinct.

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