
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
Define: In the sequence $\{a_{n}\}$, $\frac{{a_{n+2}}}{{a_{n+1}}}-\frac{{a_{n+1}}}{{a_n}}=d$ ($n\in{N^*}$), where $d$ is a constant. If this condition holds, the sequence $\{a_{n}\}$ is called a "geometric difference" sequence. Given a "geometric difference" sequence $\{a_{n}\}$ where $a_{1}=a_{2}=1$ and $a_{3}=3$, find $\frac{{a_{12}}}{{a_{10}}}$.

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