
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 $a$ such that the expression $\log_{y^{10}}{x^2} \cdot \log_{x^7}{y^3} \cdot \log_{y^8}{x^4} \cdot \log_{x^9}{y^6} \cdot \log_{y^5}{x^{11}}$ can be written as $a \log_y{x}$.

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