
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 $  be a natural number, and  $ A $  the set of the first  $ n $  natural numbers. Find the number of nondecreasing functions  $ f:A\longrightarrow A $  that have the property   $$  x,y\in A\implies |f(x)-f(y)|\le |x-y|.  $$  

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