
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 sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$ are arithmetic sequences, and $S_{n}=a_{1}+a_{2}+\cdots+a_{n}$ and $T_{n}=b_{1}+b_{2}+\cdots+b_{n}$ are the sums of the first $n$ terms of those sequences respectively, it is known that for all positive integers $n$, $\frac{S_{n}}{T_{n}}=\frac{3n+31}{31n+3}$.

(1) Find the value of $\frac{b_{28}}{a_{28}}$.

(2) Find all positive integers $n$ for which $\frac{b_{n}}{a_{n}}$ is an integer.

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