
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 arithmetic sequence $\{b_{n}\}$ and the sequence $\{a_{n}\}$ where all terms are positive, with $a_{1}=b_{1}=1$, $b_{2}+b_{4}=10$, and satisfying the equation $a_{n}^{2}-2a_{n}a_{n+1}+a_{n}-2a_{n+1}=0$.

1. Find the general term formulas for $\{a_{n}\}$ and $\{b_{n}\}$.
2. If $c_{n}= \frac {1}{a_{n}}+b_{n}$, find the sum of the first $n$ terms of the sequence $\{c_{n}\}$.

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