
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
<span style="color:darkred">Let  $n$  and  $m$  be two natural numbers,  $m\ge n\ge 2$  . Find the number of injective functions

\[f\colon\{1,2,\ldots,n\}\to\{1,2,\ldots,m\}\]
such that there exists a unique number  $i\in\{1,2,\ldots,n-1\}$  for which  $f(i)>f(i+1)\, .$ </span>

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