
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 that the sequence $\left\{a_{n}\right\}$ is an arithmetic sequence with a common difference not equal to $0$, satisfying $a_{1}=5$, and $a_{2}$, $a_{9}$, $a_{30}$ form a geometric sequence.

1. Find the general formula for $\left\{a_{n}\right\}$.
2. If the sequence $\left\{b_{n}\right\}$ satisfies $b_{n+1}-b_{n}=a_{n}$ for $n\in \mathbb{N}^{*}$, and $b_{1}=3$, find the sum of the first $n$ terms of the sequence $\left\{\dfrac{1}{b_{n}}\right\}$ denoted as $T_{n}$.

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