
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 $f(x) = x^2 + 5x + 2$ and $g(x) = x^2 + x + 2$. Let $S$ be the set of integers $\{0, 1, 2, \dots , 30\}$. Find the number of members $s$ of $S$ such that $f(s)$ is divisible by $4$ and $g(s)$ is divisible by $3$.
A) 0
B) 4
C) 8
D) 12
E) 16

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