
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 an arithmetic sequence whose first three terms are $a$, $4$, and $3a$, and the sum of its first $n$ terms is $S_{n}$. If $S_{k}=90$.

(1) Find the values of $a$ and $k$.

(2) Let $b_{n}= \frac {1}{S_{n}}$, find the sum of the first $n$ terms of the sequence $\{b_{n}\}$.

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