
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 that $\frac{\log{a}}{p+1}=\frac{\log{b}}{q-1}=\frac{\log{c}}{r+1}=\log{x}$, all logarithms to the same base and $x \neq 1$. If $\frac{b^3}{a^2c} = x^y$, determine the value of $y$.
A) $3q - 2p + r\qquad$
B) $3q - 2p - r - 6 \qquad$
C) $2p - 3q + r \qquad$
D) $3q + 2p + r + 6 \qquad$
E) $2p + r - 3q$

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