
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 an arithmetic sequence $\{a_n\}$ has a first term and common difference both equal to 2, and $a_1$, $a_8$ are respectively the first and fourth terms of a geometric sequence $\{b_n\}$.
(1) Find the general formulas for the terms of sequences $\{a_n\}$ and $\{b_n\}$.
(2) Let $c_n = \frac{4}{(\log_{2}b_{n+1})a_n}$, find the sum $S_n$ of the first $n$ terms of $\{c_n\}$.

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