
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 $\{a_n\}$ with the sum of the first $n$ terms $S_n$, it is known that $S_3 = 7$ and that the sequence $a_1 + 3$, $3a_2$, and $a_3 + 4$ forms an arithmetic sequence.
(1) Find the common ratio $q$ and the general term $a_n$ of the sequence $\{a_n\}$;
(2) If the sequence $\{a_n\}$ is an increasing sequence, let $b_n = \log_2 \frac{a_{n+1}}{128}$, calculate the sum of the absolute values $|b_1| + |b_2| + \ldots + |b_n|$.

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