
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 function defined on $\mathbb{R}$, $f(x) = x^3 + \sin(x)$, and an arithmetic sequence $\{a_n\}$ with non-zero common difference such that the following algorithm can execute properly and the output result is exactly 0, please write out the general formula for the arithmetic sequence $\{a_n\}$.

```
n ← 1
S ← 0

While i ≤ 10
    x ← a_n
    S ← S + f(x)
    n ← n + 1
End While

Print S
```

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