
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
There are four rectangular containers labeled $A$, $B$, $C$, and $D$. The base areas of $A$ and $B$ are both $x^{2}$, with heights $x$ and $y$ respectively. The base areas of $C$ and $D$ are both $y^{2}$, with heights $x$ and $y$ (where $x \neq y$). A game rule is established where two players each select two containers to hold water, and the player with more water wins. The question is: Can the player who goes first win without knowing the values of $x$ and $y$? If so, how many winning strategies are there? Please provide a proof.

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