
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
Find all real three-tuple $(x, y, z)$ such that
$$
\left\{
\begin{array}{l}
x^{2} + y^{2} + 25z^{2} = 6xz + 8yz, \\
3x^{2} + 2y^{2} + z^{2} = 240.
\end{array}
\right.
$$

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