
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 a sequence $\{a_n\}$ with the sum of the first $n$ terms denoted by $S_n$, if $S_n + n = \frac{3}{2} a_n$,  
(Ⅰ) find the general term formula for the sequence $\{a_n\}$;  
(Ⅱ) let another sequence $\{b_n\}$ be defined by $b_n = a_n + \lambda (-2)^n$, and suppose $\{b_n\}$ is an increasing sequence, determine the range of values for $\lambda$.

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