
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 three points A (0, 0, 1), B (-1, 1, 1), and C (1, 2, -3) in space, find the coordinates of point M on the line AB such that CM is perpendicular to AB.

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