
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 $\\{a\_n\\}$ where all terms are positive, $a\_1=1$, $a\_4+2$ is the geometric mean of $a\_4-1$ and $a\_9+3$, and the sequence $\\{b\_n\\}$ satisfies $b\_n=λ^{n}⋅2^{a\_n}(λ≠0)$.
(1) Find the general term formula for the sequence $\\{a\_n\\}$;
(2) Find the sum of the first $n$ terms, $S\_n$, of the sequence $\\{b\_n\\}$.

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