
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 spots along a road. Each of the \( n \) drivers drives their car to their favorite spot to park. If their favorite spot is already occupied, they will park in the nearest available spot down the road. If their favorite spot and all the spots beyond it are occupied, they will drive away without parking. How many different arrays \(\left(a_{1}, a_{2}, \cdots, a_{n}\right)\) are there such that no parking spot is left empty? Here, \( a_{i} \) represents the favorite spot of the \( i \)-th driver, and \( a_{1}, a_{2}, \cdots, a_{n} \) are not necessarily distinct.

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