
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 geometric sequence $\{a_n\}$ where $a_{n} > 0$ for $n \in \mathbb{N}^*$, the common ratio $q \in (0, 1)$, and it's known that $a_1a_5 + 2a_3a_5 + a_2a_8 = 25$, and the geometric mean of $a_3$ and $a_5$ is 2.
(1) Find the general term formula of the sequence $\{a_n\}$;
(2) Suppose $b_n = \log_{2}{a_n}$ and the sum of the first $n$ terms of the sequence $\{b_n\}$ is $S_n$. Find the general term formula for the sequence $\{S_n\}$.

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