
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
\(\left(\left(a^{1/2} - b^{1/2}\right)^{-1}\left(a^{3/2} - b^{3/2}\right) - \frac{1}{(\sqrt{a} + \sqrt{b})^{-2}}\right) : \sqrt[3]{ab \sqrt{ab}} + \frac{1}{1+\left(a(1-a^2)^{-1/2}\right)^2}\)

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