
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
For nonnegative real numbers  $x,y,z$  and  $t$  we know that  $|x-y|+|y-z|+|z-t|+|t-x|=4$ .
Find the minimum of  $x^2+y^2+z^2+t^2$ .

*proposed by Mohammadmahdi Yazdi, Mohammad Ahmadi*

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