
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 the arithmetic sequence $\{a_n\}$, $2a_1+3a_2=11$ and $2a_3=a_2+a_6-4$. Find the formula for the general term of the sequence $\{a_n\}$ and the sum of the first $n$ terms, denoted as $S_n$.

(1) Find the formula for the general term of the sequence $\{a_n\}$.

(2) Let the sequence $\{b_n\}$ satisfy $b_n= \frac{1}{S_n+n}$. Find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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