
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:

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

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