
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
A has a box containing $x$ red balls and $y$ white balls ($x, y \geq 0$, and $x + y = 4$); B has a box containing 2 red balls, 1 white ball, and 1 yellow ball. Now, A draws 2 balls from their box, and B draws 1 ball from their box. If the 3 balls drawn are all of different colors, then A wins.  
(1) How should A arrange the number of balls of the two colors in the box to maximize their chances of winning?  
(2) Under the condition of (1), calculate the expected number of red balls among the 3 balls drawn.

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