
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
What constant $k$ does the expression $\log_{y^4}{x^2}\cdot \log_{x^6}{y^3}\cdot \log_{y^3}{x^4}\cdot \log_{x^2}{y^4}\cdot \log_{y}{x^6}$ equal when written as $k\log_y{x}$?

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