
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
Consider the quintic polynomial:
\[ 16x^5 - 4x^4 - 4x - 1 = 0 \]
This equation has a real root of the form \(\frac{\sqrt[5]{a} + \sqrt[5]{b} + 1}{c}\), where \(a\), \(b\), and \(c\) are positive integers. Find \(a + b + c\).

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