
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
\[ 2 \log_{a}^{\frac{1}{2}} b \cdot \left( \left( \log_{a} \sqrt[4]{ab} + \log_{b} \sqrt[4]{ab} \right)^{\frac{1}{2}} - \left( \log_{a} \sqrt[4]{\frac{b}{a}} + \log_{b} \sqrt[4]{\frac{a}{b}} \right)^{\frac{1}{2}} \right), \ \ a, b > 1. \]

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