
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 the sequence ${{a_{n}}}$, where ${a_{n+1} = a_{n} + 4}$, and ${a_{1} + a_{4} = 14}$.

(1) Find the general term formula ${a_{n}}$ and the sum of the first $n$ terms ${s_{n}}$.

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

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