
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 sequence $\left\{ a_n \right\}$ that satisfies: $a_1=3$, $(2n-1)a_n+2=(2n+1)a_{n-1}+8n^2$ $(n > 1,n\in \mathbb{N}^*)$, and let $b_n=\frac{1}{a_n}$, find the range of values for the sum of the first n terms of the sequence $\left\{ b_n \right\}$.

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