
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
Given real numbers \( a, b, c, d \) satisfying \( a^{2} + b^{2} + c^{2} + d^{2} = 5 \), find the maximum value of \( (a - b)^{2} + (a - c)^{2} + (a - d)^{2} + (b - c)^{2} + (b - d)^{2} + (c - d)^{2} \).

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