
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 triples of reals  $(x,y,z)$  satisfying:  $$ \begin{cases}
\frac{1}{3} \min \{x,y\} + \frac{2}{3} \max \{x,y\} = 2017 
\frac{1}{3} \min \{y,z\} + \frac{2}{3} \max \{y,z\} = 2018 
\frac{1}{3} \min \{z,x\} + \frac{2}{3} \max \{z,x\} = 2019 
\end{cases} $$  

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