
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
Let \( a, b, c, d \) be real numbers such that \( a^{2}+b^{2}+c^{2}+d^{2}=1 \). Determine the minimum value of \( (a-b)(b-c)(c-d)(d-a) \) and determine all values of \( (a, b, c, d) \) such that the minimum value is achieved.

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