
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 the function f(x) = x^2^ - 2x + 2, the sequence {a_n} is an arithmetic sequence where a_2 = f(3) and a_3 is the minimum value of f(x).

1. Find the general term formula for {a_n}.
2. If {b_n} is a geometric sequence with positive terms, where b_1 = a_3 and b_3 = a_1, find the general term formula for {b_n} and the sum of the first n terms for {a_n + b_n}, denoted as S_n.

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