
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 \( x_{1}, \ldots, x_{n} \in (0,1) \), find the maximum value of the expression

$$
A = \frac{\sqrt[4]{1-x_{1}} + \ldots + \sqrt[4]{1-x_{n}}}{\frac{1}{\sqrt[4]{x_{1}}} + \ldots + \frac{1}{\sqrt[4]{x_{n}}}}
$$

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