
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
Given a point A (-1, -1, 2) in the three-dimensional Cartesian coordinate system, and a point B is a moving point on the line x+y=1 in the xOy plane, find the shortest distance between points A and B.

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