
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 general term of the sequence $\\_a\_n\_$ is $a\_n = 2n + 1$. Define a new sequence $\_b\_n\_$ as the average of the first $n$ terms of $\_a\_n\_$, i.e., $b\_n = \frac{a\_1 + a\_2 + a\_3 + ... + a\_n}{n}$ for $n \in \mathbb{N}^+$. 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