
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
Music is composed of sounds of different frequencies. If the frequency of the first note $1(do)$ is $f$, then the frequencies of the seven notes $1(do)$, $2(re)$, $3(mi)$, $4(fa)$, $5(so)$, $6(la)$, $7(si)$ in the solfège are $f$, $\frac{9}{8}f$, $\frac{81}{64}f$, $\frac{4}{3}f$, $\frac{3}{2}f$, $\frac{27}{16}f$, $\frac{243}{128}f$. The ratio of the frequency of the latter note to the former note is the interval between two adjacent notes. The intervals of the seven notes mentioned above have only two different values, denoted as $\alpha$ and $\beta (\alpha > \beta)$. $\alpha$ is called a whole tone, and $\beta$ is called a semitone. Then $\lg \alpha^{5} + \lg \beta^{2} - \lg 2 = \_\_\_\_\_$.

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