
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 following system of equations:

$$
\begin{aligned}
a^{3} x + a^{2} y + a z + u & = 1 \\
b^{3} x + b^{2} y + b z + u & = 0 \\
c^{3} x + c^{2} y + c z + u & = 0 \\
d^{3} x + d^{2} y + d z + u & = 0
\end{aligned}
$$

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