
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
There is a set of data: $a_{1}=\frac{3}{1×2×3}$, $a_{2}=\frac{5}{2×3×4}$, $a_{3}=\frac{7}{3×4×5}$, $\ldots$, $a_{n}=\frac{2n+1}{n(n+1)(n+2)}$. Let $S_{n}=a_{1}+a_{2}+a_{3}+\ldots +a_{n}$, find the value of $S_{12}$.

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