
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
(1) In the expansion of ${(1+x)^{n}}$, if the coefficient of the third term is equal to that of the sixth term, what is the value of $n$?
(2) In the expansion of ${(x\sqrt{x}-\frac{2}{\sqrt{x}})}^{n}$, the sum of the binomial coefficients of the odd terms is 128. Find the maximum binomial coefficient term in the expansion.

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