
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 $\{a\_n\}$ with the sum of its first $n$ terms, $S\_n = n^2 + kn$, where $k \in \mathbb{N}^*$, and the minimum value of $S\_n - 5kn$ is $-4$.

1. Find the general formula for the $n$-th term of the sequence $\{a\_n\}$.
2. Let $b\_n = \frac{a\_n}{4^n}$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$.

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