
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 the sequence $\{a_n\}$ satisfies $a_{n+1}+a_{n-1}\leq 2a_n$ ($n\in\mathbb{N}^*$, $n\geq 2$), find the range of values for $d$ such that the sequence $\left\{\frac{b_n}{n}\right\}$ is convex, where $\{b_n\}$ is an arithmetic sequence with a common difference of $\ln d$ and the first term $b_1=2$.

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