
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
Zhu Zaiyu (1536-1611), the ninth generation descendant of the Ming Dynasty, was a musician, mathematician, and astronomer. Among his extensive writings, he is most famous for his work "Complete Book of Music Theory." In the eyes of Westerners, he was considered a scholar prince with encyclopedic knowledge. His greatest contribution to the arts was the creation of the "twelve-tone equal temperament," a theory widely used in keyboard instruments around the world, including the piano. Therefore, Zhu Zaiyu is known as the "ancestor of piano theory." The "twelve-tone equal temperament" refers to an octave with 13 notes, where the frequency ratio between adjacent notes is equal, and the frequency of the last note is twice that of the initial note. If the frequency of the second note is $f_{2}$ and the frequency of the eighth note is $f_{8}$, then $\frac{{f_{8}}}{{f_{2}}}$ is ______.

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