
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
In the arithmetic sequence $\{a_{n}\}$, $a_{7}=4$, and $a_{19}=2a_{9}$.
1. Find the general term formula for $\{a_{n}\}$.
2. Let $b_{n}=\frac{1}{2na_{n}}$. 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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