
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
Solve the system of equations:

$$
\begin{aligned}
& \log _{a} x-\log _{b} y=m, \\
& \log _{b} x-\log _{c} y=n, \quad \text{where } b=a^{2}, c=a^{3}
\end{aligned}
$$

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