
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 \( A = \{1, 2, \cdots, n\} \) (where \( n > 1 \) and \( n \in \mathbf{N} \)). Consider a function \( f: A \rightarrow A \). The number of functions \( f \) that satisfy 
\[ f(1) \leqslant f(2) \leqslant \cdots \leqslant f(n), \]
and take exactly \( k \) (\( 1 < k \leqslant n \)) different values is?

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