
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
Knowing that the system
$$
\begin{aligned}
x+y+z & =3, \\
x^{3}+y^{3}+z^{3} & =15, \\
x^{4}+y^{4}+z^{4} & =35,
\end{aligned}
$$
has a real solution \( x, y, z \) for which \( x^{2}+y^{2}+z^{2}<10 \), find the value of \( x^{5}+y^{5}+z^{5} \) for that solution.

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