
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
Evaluate the expression using logarithmic theorems:
\[\log{\frac{a^2}{b}} + \log{\frac{b^3}{c^2}} + \log{\frac{c}{d}} + \log{\frac{d^2}{e}} - \log{\frac{a^3y}{e^2x}}\]
A) $\log\left(\frac{x^2}{y^2}\right)$
B) $\log\left(\frac{b^2 ex}{c a y}\right)$
C) $\log\left(\frac{x}{y}\right)$
D) $\log\left(\frac{a^2}{b^2}\right)$
E) None of the above

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