
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
In the arithmetic sequence $\{a_{n}\}$, with a common difference $d\neq 0$, and $a_{7}$, $a_{10}$, $a_{15}$ being the consecutive $3$ terms of the geometric sequence $\{b_{n}\}$, then when $b_{1}=3$, $b_{n}=\_\_\_\_\_\_$.

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