
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 sequence ${a_n}$ where $a_1=\frac{1}{2},a_{n+1}=a_n+\frac{1}{n^2+3n+2}\ (n\in\mathbb{N}^*)$, find the general term of the sequence ${a_n}$.

A) ${a_n=\frac{1}{n+1}}$

B) ${a_n=\frac{n}{n+1}}$

C) ${a_n=\frac{1}{2}+\frac{n-1}{n^2+n+2}}$

D) ${a_n=\frac{n+1}{n+2}}$

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