
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) Find the distance from the point \((1,0)\) to the line connecting the origin and the point \((0,1)\).

(b) Find the distance from the point \((1,0)\) to the line connecting the origin and the point \((1,1)\).

(c) Find the distance from the point \((1,0,0)\) to the line connecting the origin and the point \((1,1,1)\).

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