
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 $\left\{ {{a}\_{n}} \right\}$ that satisfies $\frac{1}{{{a}\_{n+1}}}-\frac{1}{{{a}\_{n}}}=d(n\in {{N}^{\*}},d\)$ is a constant, it is called a harmonic sequence. Now, there is a harmonic sequence $\left\{ {{b}\_{n}} \right\}$ that satisfies ${{b}\_{1}}=1,{{b}\_{2}}=\frac{1}{2}$.

(1) Find the general term formula for $\left\{ {{b}\_{n}} \right\}$;

(2) If the sequence ${{c}\_{n}}=\frac{{{b}\_{n}}}{n+2}$, find the sum of the first $n$ terms of $\left\{ {{c}\_{n}} \right\}$ (${{S}\_{n}}$).

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