
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
Let's solve the following system of equations among positive numbers:

$$
\begin{aligned}
& x + y^{2} + z^{3} = 3, \\
& y + z^{2} + x^{3} = 3, \\
& z + x^{2} + y^{3} = 3.
\end{aligned}
$$

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