
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?

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