
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 $xOy$, the polyline distance between two points $A(x_1, y_1)$ and $B(x_2, y_2)$ is defined as $d(A, B) = |x_1 - x_2| + |y_1 - y_2|$. Given point $O(0, 0)$ and $C(x, y)$, with $d(O, C) = 1$, the range of values for $\sqrt{x^2 + y^2}$ is ______.

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