
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
In an arithmetic sequence $\{a_n\}$, $a_2=5$ and $a_6=21$.  
(1) Find the general formula for the nth term $a_n$ and the sum of the first n terms $S_n$.  
(2) Let $b_n = \frac{2}{S_n+5n}$, find the sum of the first n terms $T_n$ for the sequence $\{b_n\}$.

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