
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 a roadside, there are $n$ parking spots. Each of the $n$ drivers parks their car in their favorite spot. If the favorite spot is already taken, they will park their car in the nearest available spot further along the road. If there are no available spots further along, they will drive away and not park at all. How many different sequences $\left(a_{1}, a_{2}, \cdots, a_{n}\right)$ are there such that no parking spot is left empty? Here, $a_{i}$ represents the favorite parking spot of the $i$-th driver, and $a_{1}, a_{2}, \cdots, a_{n}$ do not need to be distinct.

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