
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 \\(a > 0\\), \\(b > 0\\), and \\(a+4b={{(ab)}^{\\frac{3}{2}}}\\).

\\((\\)I\\()\\) Find the minimum value of \\(a^{2}+16b^{2}\\);

\\((\\)II\\()\\) Determine whether there exist \\(a\\) and \\(b\\) such that \\(a+3b=6\\), and explain the reason.

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