
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
\[
\left(6 \left(\log_b a \cdot \log_{a^2} b+1\right) + \log_a b^{-6} + \log_a^2 b\right)^{1/2} - \log_a b \quad \text{for} \quad a > 1.
\]

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