
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
Non-negative real numbers \( x_{1}, x_{2}, \cdots, x_{2016} \) and real numbers \( y_{1}, y_{2}, \cdots, y_{2016} \) satisfy:
(1) \( x_{k}^{2}+y_{k}^{2}=1 \) for \( k=1,2, \cdots, 2016 \);
(2) \( y_{1}+y_{2}+\cdots+y_{2016} \) is odd.

Find the minimum value of \( x_{1}+x_{2}+\cdots+x_{2016} \).

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