
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 an arithmetic sequence $\{a_n\}$ with common difference $d$, and $d>0$, and a geometric sequence $\{b_n\}$ with common ratio $q$, and $q>1$, the first term $b_1>0$. If $a_n-a_1>\log_{a}b_n-\log_{a}b_1$ ($n\in\mathbb{N}$, $n>1$, $a>0$, $a\neq1$), find the range of the real number $a$.

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