
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
Cut a 12cm long thin iron wire into three segments with lengths a, b, and c,  
(1) Find the maximum volume of the rectangular solid with lengths a, b, and c as its dimensions;  
(2) If these three segments each form an equilateral triangle, find the minimum sum of the areas of these three equilateral triangles.

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