
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
Let the sequence \\(\{a_n\}\) be defined as \\(a_1=2\\), \\(a_{n+1}= \dfrac{2}{a_n+1}\\), \\(b_n=\left| \dfrac{a_n+2}{a_n-1} \right|\), \\(n\in\mathbb{N}^*\), then the general formula for the sequence \\(\{b_n\}\) is \\(b_n=\)\_\_\_\_\_\_\_\_\_\_.

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