
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 numbers \( x \) and \( y \) in the interval \( \left(0, \frac{\pi}{2}\right) \), find the maximum value of the expression

$$
A = \frac{\sqrt[4]{\sin x \sin y}}{\sqrt[4]{\tan x} + \sqrt[4]{\tan y}}
$$

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