
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 $A$, $B$, $C$, $D$, with the base areas of $A$ and $B$ both being $a^{2}$, and their heights being $a$ and $b$ respectively; the base areas of $C$ and $D$ are both $b^{2}$, with heights being $a$ and $b$ ($a\neq b$). A game rule is set: player A chooses two of these four containers, and the remaining two are given to player B. The winner is the one with more water. Does player A have a winning strategy? If so, how many are there? Please write down the calculation process. (Hint: $a^{3}+b^{3}=\left(a+b\right)(a^{2}-ab+b^{2})$)

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