
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 sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n = 2^n + a$ (where $a$ is a constant and $n \in \mathbb{N}^*$).

1. Find $a\_1$, $a\_2$, and $a\_3$.
2. If the sequence $\{a\_n\}$ is a geometric sequence, find the value of the constant $a$ and the expression for $a\_n$.
3. For $a\_n$ obtained in part (2), let $f(n) = λ \cdot a_{2n+1} - 4λ \cdot a_{n+1} - 3$. If $f(n) < 0$ holds true for any positive integer $n$, find the range of real number $λ$.

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