
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
In the plane, a square $A B C D$ with side length $a$ and a point $M$ at a distance $b$ from its center are given. Find the sum of the volumes of the solids obtained by rotating the triangles $A B M, B C M, C D M$, and $D A M$ around the lines $A B, B C, C D$, and $D A$, respectively.

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