
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
\(\left(\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}\right)^{-1} \cdot\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}\right)^{1 / 2}-\sqrt{a-1} \cdot(\sqrt{a}+1)^{-1}\right)^{-2} \cdot \frac{1}{a^{2 / 3}+a^{1 / 3}+1}\).

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