
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 sequence $\{a_n\}$ with the first term $a_1=1$, for $\forall n\in \mathbb{N}_+$, the point $(a_n,a_{n+1})$ is on the graph of the function $f(x)=2x+1$.

(1) Find the general term of the sequence $\{a_n\}$;

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

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