
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 $\{a\_n\}$ and $\{b\_n\}$ are both arithmetic sequences with their respective sums of the first $n$ terms being $S_n$ and $T_n$, if for any $n ∈ ℕ^*$, $\frac{S_n}{T_n} = \frac{31n + 101}{n + 3}$, determine the set of positive integers $n$ for which $\frac{a_n}{b_n}$ is an integer.

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