
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 $\frac{1}{a} + \frac{1}{b} = \sqrt{ab}$,

(I) Find the minimum value of $a^{3} + b^{3}$;

(II) Determine whether there exist $a, b$ such that $2a + 3b = 6$, and explain the reason.

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