
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 first three terms of an arithmetic sequence are $m$, $4$, and $3m$, respectively, and the sum of the first $n$ terms is $S_{n}$, with $S_{k}=110$.

(1) Find the values of $m$ and $k$.
(2) Let the sequence ${b_{n}}$ have a general term $b_{n}=\frac{S_{n}}{n}$ and be an arithmetic sequence. Find the sum of its first $n$ terms, $T_{n}$.

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