
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 that the sum of the first $n$ terms of the sequence ${a_{n}}$ is $S_{n}$, the first term is $a_{1}$, and $\frac{1}{2}$, $a_{n}$, $S_{n}$ form an arithmetic sequence.

1. Find the general term formula for the sequence ${a_{n}}$.
2. The sequence ${b_{n}}$ satisfies $b_{n}=(\log_{2}a_{2n+1})(\log_{2}a_{2n+3})$. Find the sum of $\frac{1}{b_{1}}+\frac{1}{b_{2}}+\frac{1}{b_{3}}+\cdots +\frac{1}{b_{n}}$.

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