
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 a positive arithmetic sequence $\left\{a_n\right\}$ with the sum of the first $n$ terms denoted as $S_n$, and it satisfies $a_1+a_5= \frac{2}{7}a_3^2, S_7=63$,

  (1) Find the general formula for the sequence $\left\{a_n\right\}$;

  (2) If the sequence $\left\{b_n\right\}$ satisfies $b_1=a_1, b_{n+1}-b_n=a_{n+1}$, find the sum of the first $n$ terms of the sequence $\left\{ \frac{1}{b_n}\right\}$, denoted as $T_n$.

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