
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
Rationalize the denominator of \(\frac{1}{\sqrt[4]{4} - \sqrt[4]{2}}\). With your answer in the form \(\frac{\sqrt[4]{X} + \sqrt[4]{Y} + \sqrt[4]{Z} + \sqrt[4]{W}}{D}\), and the fraction in lowest terms, what is \(X + Y + Z + W + D\)?

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