
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 the sum of the first $n$ terms, $S_n$, of the positive sequence $\{a_n\}$ satisfies $2S_n = a_{n+2} - 2$, where $n \in \mathbb{N}^*$.

1. If the sequence $\{a_n\}$ is a geometric sequence, find the common ratio $q$ of the sequence $\{a_n\}$.
2. If $a_2 = a_1 = 1$ and $b_n = a_n + a_{n+1}$, find the general term formula of the sequence $\{b_n\}$.

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