
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 constant $k$ such that the expression $\log_{y^4}{x} \cdot \log_{x^3}{y^6} \cdot \log_{y^3}{x^2} \cdot \log_{x^2}{y^3} \cdot \log_{y^6}{x^3}$ can be written as $k \log_y{x}$.

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