
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
Given positive integers \( m \) and \( n \) satisfying \( m \geq n \geq 2 \), find the number of injective functions \( f: \{1, 2, \ldots, n\} \rightarrow \{1, 2, \ldots, m\} \) such that there is exactly one \( i \in \{1, 2, \ldots, n-1\} \) for which \( f(i) > f(i+1) \). 

(Romanian Mathematical Olympiad, 2012)

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