
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 system
$$\left\{\begin{array}{l}x^{\prime}=3x-y+z, \\ y^{\prime}=-x+5y-z, \\ z^{\prime}=x-y+3z\end{array}\right.$$

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