
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
Let $\{a\_n\}$ be a geometric sequence with a common ratio of $q (q > 0$ and $q \neq 1)$, and the sequence $4a\_1$, $3a\_2$, $2a\_3$ forms an arithmetic sequence. The sum of the first 4 terms of this sequence is $S\_4 = 15$.
(1) Find the general term formula for $\{a\_n\}$;
(2) Let $b\_n = a\_n + 2n (n = 1, 2, 3, ...)$, find the sum of the first $n$ terms for $\{b\_n\}$.

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