
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
How many possible bijections \( f \) on \(\{1, 2, \dots, n\}\) are there such that for each \( i = 2, 3, \dots, n \), we can find \( j < i \) with \( f(i) - f(j) = \pm 1\)?

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