
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
Determine the value of $b$ such that the expression $\log_{y^8}{x^2}\cdot\log_{x^7}{y^4}\cdot\log_{y^6}{x^5}\cdot\log_{x^5}{y^6}\cdot\log_{y^4}{x^7}$ can be written as $b\log_y{x}$.

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