
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 $\sqrt{a}, \sqrt{b}$ ($a > b > 0$) are the two real roots of the equation $x^2 - 5x + 2 = 0$, find the value of $$\frac{a\sqrt{a} + b\sqrt{b}}{a - b}\left(\frac{2}{\sqrt{a}} - \frac{2}{\sqrt{b}}\right) \div \left(\sqrt{a} - \frac{a + b}{\sqrt{b}}\right) + \frac{5(5\sqrt{a} - a)}{b + 2}.$$

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