
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
Find positive integers \(d\), \(e\), \(f\), and \(g\) such that
\[
3 \sqrt{\sqrt[3]{7} + \sqrt[3]{6}} = \sqrt[3]{d} - \sqrt[3]{e} + \sqrt[3]{f} + \sqrt[3]{g}.
\]
Determine \(d + e + f + g.\)

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