
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 a Cartesian coordinate system on a plane, O is the origin, the magnitudes of the vectors $\overrightarrow{OB}$, $\overrightarrow{OC}$, and $\overrightarrow{OD}$ are all equal to 1, and $\overrightarrow{OB} + \overrightarrow{OC} + \overrightarrow{OD} = \overrightarrow{0}$. Given A(1, 1), find the range of values for the dot product $\overrightarrow{AD} \cdot \overrightarrow{OB}$.

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