
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 points \( A(1, -1, 0) \) and \( B(2, 0, 1) \) are on skew lines \( a \) and \( b \) respectively, and the direction vectors of lines \( a \) and \( b \) are \(\boldsymbol{a} = (1, 0, -1)\) and \(\boldsymbol{b} = (1, -1, 1)\) respectively. Find the distance between the two skew lines \( a \) and \( b \).

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