
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
Given $\left( x^{2}+\frac{2}{x} \right)^{n}$, where $n\in \mathbb{N}^{*}$.
(I) When $n=6$, find the constant term in the binomial expansion;
(II) If the binomial coefficients of the third and seventh terms in the binomial expansion of $\left( x^{2}+\frac{2}{x} \right)^{n}$ are equal, find the coefficient of the middle term in the expansion.

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