
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
\[
\left(\frac{\left(1+a^{-1 / 2}\right)^{1 / 6}}{\left(a^{1 / 2}+1\right)^{-1 / 3}}-\frac{\left(a^{1 / 2}-1\right)^{1 / 3}}{\left(1-a^{-1 / 2}\right)^{-1 / 6}}\right)^{-2} \cdot \frac{\frac{1}{3} \cdot a^{1 / 12}}{\sqrt{a}+\sqrt{a-1}}
\]

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