
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
\[
\frac{\log _{a} b+\log _{a}\left(b^{1 / 2 \log _{b} a^{2}}\right)}{\log _{a} b-\log _{a b} b} \cdot \frac{\log _{a b} b \cdot \log _{a} b}{b^{2 \log _{b} \log _{a} b}-1}
\]

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