
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 first term $a\_1=1$, common difference $d > 0$, and the second, fifth, and fourteenth terms are the second, third, and fourth terms of a geometric sequence $\{b\_n\}$, respectively.

1. Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$.
2. Suppose a sequence $\{c\_n\}$ satisfies $\frac{c\_1}{b\_1} + \frac{c\_2}{b\_2} + \dots + \frac{c\_n}{b\_n} = a\_{n+1}$ for all positive integers $n$. Find the sum $c\_1 + c\_2 + c\_3 + \dots + c\_{2016}$.

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