
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 $\{a_n\}$ is a geometric sequence with a positive common ratio, $a_1 = 2$, and $a_3 = a_2 + 4$.

(1) Find the general term formula for $\{a_n\}$.

(2) If $\{a_n\}$ is an arithmetic sequence with the first term $1$ and common difference $2$, find the sum of the first $n$ terms for the sequence $\{a_n + b_n\}$.

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