
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 a sequence $\{a_n\}$ where $a_1= \frac {1}{2}$ and $(n+1)(na_n \cdot a_{n+1}+a_{n+1})-na_n=0$ $(n \in \mathbb{N^*})$, let the sum of the first $n$ terms of the sequence $\left\{ \frac {a_n}{n+2} \right\}$ be $S_n$. Find the expression for $S_n$.

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