
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
A tangent line is drawn from point P (-1, 1) to the circle C: $(x-t)^2+(y-t)^2=1$ ($t\in\mathbb{R}$), and the tangent points are A and B, respectively. The minimum value of $\overrightarrow{PA} \cdot \overrightarrow{PB}$ is \_\_\_\_\_.

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