
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
The sequence $\{a_n\}$ is a geometric sequence with an even number of terms. The sum of all terms is four times the sum of the even terms, and the product of the first three terms is $64$. Find the general formula for the $n$-th term of this sequence, which is $a_n=\_\_\_\_\_\_\_$.

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