
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
Suppose that for real  $x,y,z,t$  the following equalities hold: $\{x+y+z\}=\{y+z+t\}=\{z+t+x\}=\{t+x+y\}=1/4$ .
Find all possible values of  $\{x+y+z+t\}$ .(Here $\{x\}=x-[x]$ )

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