
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
$$
\left(\frac{a + a^{3/4} b^{1/2} + a^{1/4} b^{3/2} + b^{2}}{a^{1/2} + 2a^{1/4} b^{1/2} + b} \cdot (\sqrt[4]{a} + \sqrt{b}) + \frac{3 \sqrt{b} \left(a^{1/2} - b \right)}{a^{-1/4} \left(a^{1/4} - \sqrt{b}\right)}\right)^{-1/3} : (\sqrt[4]{a} + \sqrt{b})^{-1}
$$

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