
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 sequences $\{a_{n}\}$ and $\{b_{n}\}$, where $a_{n}=n^{2}$, $n\in\mathbb{N}^{*}$, and the terms of $\{b_{n}\}$ are distinct positive integers. If for any $n\in\mathbb{N}^{*}$, the $a_{n}$-th term of $\{b_{n}\}$ equals the $b_{n}$-th term of $\{a_{n}\}$, then the value of $\frac{\lg(b_{1}b_{4}b_{9}b_{16})}{\lg(b_{1}b_{2}b_{3}b_{4})}=$ \_\_\_\_\_\_.

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