
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 common difference $d=2$ and the sum of the first $n$ terms denoted by $S_n$. A geometric sequence $\{b_n\}$ satisfies $b_1=a_1$, $b_2=a_4$, and $b_3=a_{13}$.  
(1) Find expressions for $a_n$ and $b_n$.  
(2) Let $T_n$ denote the sum of the first $n$ terms of the sequence $\left\{\frac{1}{S_n}\right\}$. Find $T_n$.

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