
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 the following is an algorithm related to the function defined on $\mathbb{R}$, $f(x) = x^3 + \sin x$, and an arithmetic sequence $\{a_n\}$ with a non-zero common difference, such that the program can run normally and the output result is exactly 0. Please write out a formula for the general term of the sequence $\{a_n\}$ that meets the conditions.  
$n \leftarrow 1$ $S \leftarrow 0$  
While $i \leq 10$  
$x \leftarrow a_n$  
$S \leftarrow S + f(x)$  
$n \leftarrow n + 1$  
End While  
Print $S$

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