
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 an arithmetic sequence $\{a\_n\}$ with $a\_1=1$ and a common difference $d > 0$, it is known that $a\_2$, $a\_5$, and $a\_{14}$ are the second, third, and fourth terms of a geometric sequence $\{b\_n\}$.
(1) Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$.
(2) Find the sum $S\_n$ of the first $n$ terms of the sequence $\{a\_n + b\_n\}$.

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