
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
Suppose the sum of the coefficients of all terms in the expansion of \\((2 \sqrt[3]{x}-1)^{n}\\) is \\(M\\), and the sum of the binomial coefficients is \\(N\\). If \\(M\\), \\(8\\), and \\(N\\) form a geometric sequence, find the fourth term in the expansion.

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