
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 first term of 2 and a common difference of 2, and a geometric sequence $\{b_n\}$ with a first term of 1 and a common ratio of 2,
(1) Find the general formula for $\{a_n\}$ and $\{b_n\}$;
(2) Find the sum of the first $n$ terms, $S_n$, of the sequence $\left\{\frac{1}{a_na_{n+1}}\right\}$.

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