
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 $\{b_n\}$ is a monotonically increasing arithmetic sequence, $b_3 + b_8 = 26$, $b_5 b_6 = 168$, and the sequence $\{a_n\}$ satisfies $2a_1 + 2^2a_2 + 2^3a_3 + \dots + 2^na_n = 2^{b_n}$,
(1) Find the general term of the sequence $\{b_n\}$;
(2) Find the sum of the first $n$ terms of the sequence $\{a_n\}$, denoted as $S_n$.

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