
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
In the arithmetic sequence $\{a_n\}$ and the geometric sequence $\{b_n\}$, it is given that $a_1 = 1$, $b_1 = 2$, $b_n > 0$ (for $n \in \mathbb{N}^*$). Additionally, $b_1, a_2, b_2$ form an arithmetic sequence and $a_2, b_2, a_3 + 2$ form a geometric sequence. The sum of the first $n$ terms of the sequence $\{b_n\}$ is denoted by $S_n$.

(Ⅰ) Find the general term formulas for the sequences $\{a_n\}$ and $\{b_n\}$.

(Ⅱ) If for every positive integer $n$, the inequality $S_n + a_n > m$ is always true, determine the range of values for the constant $m$.

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