
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
Among the permutations of integers $1, 2, \cdots, n$, how many permutations are there such that each number is either greater than all the numbers preceding it or less than all the numbers preceding it?

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