
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
Given $\frac{\log{a}}{p} = \frac{\log{b}}{q} = \frac{\log{c}}{r} = \log{x}$, where all logarithms are to the same base and $x \neq 1$, and $\frac{b^3}{a^2c} = x^y$, express $y$ in terms of $p$, $q$, and $r$.

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