
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
If \((a, b)\) is the solution of the system \(\sqrt{x+y} + \sqrt{x-y} = 4\) and \(x^2 - y^2 = 9\), then \(\frac{ab}{a+b}\) has what value?
(a) \(\frac{10}{9}\)
(b) \(\frac{8}{3}\)
(c) 10
(d) \(\frac{20}{9}\)

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