
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

Given \( x_{k}, y_{k} \geqslant 0\) for \( k = 1, 2, 3 \), calculate the minimum value of:

\[
\sqrt{(2018 - y_{1} - y_{2} - y_{3})^{2} + x_{3}^{2}} + \sqrt{y_{3}^{2} + x_{2}^{2}} + \sqrt{y_{2}^{2} + x_{1}^{2}} + \sqrt{y_{1}^{2} + (x_{1} + x_{2} + x_{3})^{2}}
\]

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