
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
The sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ is $S_n$, and it is given that $S_5=45$ and $S_6=60$.  
(1) Find the general formula for $a_n$;  
(2) If the sequence $\{a_n\}$ satisfies $b_{n+1}-b_n=a_n$ ($n\in\mathbb{N}^*$) and $b_1=3$, find the sum of the first $n$ terms of $\left\{ \frac{1}{b_n} \right\}$, denoted as $T_n$.

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