
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

For \( x, y \in (0,1] \), find the maximum value of the expression

\[ 
A = \frac{\left(x^{2} - y\right) \sqrt{y + x^{3} - x y} + \left(y^{2} - x\right) \sqrt{x + y^{3} - x y} + 1}{(x - y)^{2} + 1} 
\]

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