
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 $f(x) = x^3 + 2x^2 + 3x + 2$, and let S be the set of integers $\{0, 1, 2, \ldots, 30\}$. Determine the number of members $s$ of $S$ such that $f(s)$ leaves a remainder of zero when divided by $10$.
A) 10
B) 12
C) 14
D) 16
E) 18

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