
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
$$
\frac{1}{3} \log (a x+b y)+\log (a x-b y)=\frac{1}{2}[\log (\sqrt{a x}+\sqrt{b y})+\log (\sqrt{a x}-\sqrt{b y})]
$$

$$
\log x-\log a=\log y-\log b
$$

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