
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
Find a sequence $\{f(n)\}_{n \geqslant 0}$ such that its first 5 terms are $1, 3, 7, 13, 21$. Determine the general term $f(n)$ as a polynomial of $n$ with the lowest possible degree.

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