
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
Let  $n\ge 2$  be a positive integer. Find the number of functions  $f:\{1,2,\ldots ,n\}\rightarrow\{1,2,3,4,5 \}$  which have the following property:  $|f(k+1)-f(k)|\ge 3$ , for any  $k=1,2,\ldots n-1$ .

*Vasile Pop*

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