
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
Four equations with four unknowns. Find all solutions to the following system of equations:

$$
\left\{\begin{aligned}
x + y + z + w & = 10 \\
x^2 + y^2 + z^2 + w^2 & = 30 \\
x^3 + y^3 + z^3 + w^3 & = 100 \\
x y z w & = 24
\end{aligned}\right.
$$

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