
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
In the Cartesian coordinate system, define $d(P,Q)=|x_{1}-x_{2}|+|y_{1}-y_{2}|$ as the "polyline distance" between two points $P(x_{1},y_{1})$ and $Q(x_{2},y_{2})$. Then, the minimum "polyline distance" between a point on the circle $x^{2}+y^{2}=1$ and a point on the line $2x+y-2 \sqrt {5}=0$ is ______.

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