
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 $\\{a_n\\}$ where the sum of the first $n$ terms is $S_n = \frac{1}{7}(2^{3n+1}-2)$ for $n \in \mathbb{N}^*$,
1. Find the general term formula for the sequence $\\{a_n\\}$.
2. Let $b_n = \log_2{a_n}$, calculate the value of $\sum_{k=1}^n \frac{1}{b_k b_{k+1}}$.

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