
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 $\{a_n\}$, where $a_n > 0$ and the common difference $d > 0$, it is given that $a_4 \cdot a_6 > a_3 \cdot a_7$. By analogy with the above property, in the geometric sequence $\{b_n\}$, where $b_n > 0$ and $q > 1$, write down an inequality involving $b_5$, $b_7$, $b_4$, and $b_8$.

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