
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 the sequence $\{a_n\}$ have a sum of the first $n$ terms denoted as $S_n$. It is known that $a_1 = a$, $a_{n+1} = S_n + 3^n$, where $n \in \mathbb{N}^*$. Based on this,  
(Ⅰ) Let $b_n = S_n - 3^n$, find the general formula for the sequence $\{b_n\}$.  
(Ⅱ) If $a_{n+1} \geq a_n$, where $n \in \mathbb{N}^*$, find the range of values for $a$.

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