
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 a sequence $\{a_n\}$ with the sum of its first $n$ terms $S_n = \frac{n^2 + 3n}{4}$, for $n \in \mathbb{N}^*$,
1. Find the general formula for the $n$-th term of the sequence $\{a_n\}$;
2. Let $b_n = (n+1)\cdot4^{a_n} - \frac{1}{4a_na_{n+1}}$, find the sum of the first $n$ terms of the sequence $\{b_n\}$.

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