
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 that the expansion of \\({\left( \sqrt{x}+ \frac{2}{{x}^{2}}\right)}^{n} \\) contains only one term whose binomial coefficient is the largest at the sixth term.

\\((1)\\) Find the number of rational terms in the expansion;

\\((2)\\) Find the term with the largest coefficient in the expansion.

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