
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
The terms of the sequence ${a_n}$ are all positive numbers, and for any $n \in \mathbb{N}^*$ and $n \geq 2$, the three numbers $\frac{1}{2}a_n^2$, $a_{n-1}^2$ form an arithmetic sequence. Also, $a_1 = 1$.
(1) Find the general term formula for the sequence ${a_n}$:
(2) If the sequence ${b_n}$ satisfies $b_n = \frac{1}{a_n + a_{n+1}}$, find the sum of the first $n$ terms, $S_n$, of the sequence ${b_n}$.

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