
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 a rearrangement of the numbers from  $1$  to  $n$ , each pair of consecutive elements  $a$  and  $b$  of the sequence can be either increasing (if  $a < b$ ) or decreasing (if  $b < a$ ). How many rearrangements of the numbers from  $1$  to  $n$  have exactly two increasing pairs of consecutive elements? Express your answer in terms of  $n$ .

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