
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
Solve the system of four equations with four unknowns:
$$
\begin{array}{rr}
|a-b| y+|a-c| z+|a-d| t & =1 \\
|b-a| x+|b-c| z+|b-d| t & =1 \\
|c-a| x+|c-b| y+|c-d| t & =1 \\
|d-a| x+|d-b| y+|d-c| z & =1
\end{array}
$$
where \(a, b, c, d\) are some four pairwise distinct real numbers.

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