
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 an integer bigger than  $0$ . Let  $\mathbb{A}= ( a_1,a_2,...,a_n )$  be a set of real numbers. Find the number of functions  $f:A \rightarrow A$  such that  $f(f(x))-f(f(y)) \ge x-y$  for any  $x,y \in \mathbb{A}$ , with  $x>y$ .

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