
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 \(a < b < c < d\) and \((x, y, z, t)\) be any permutation of \((a, b, c, d)\). How many different values can the expression
$$
n = (x - y)^2 + (y - z)^2 + (z - t)^2 + (t - x)^2
$$
take?

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