
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 in space $A(0,0,1)$, $B(-1,1,1)$, and $C(1,2,-3)$, if a point $M$ on the line $AB$ satisfies $CM \perp AB$, then the coordinates of point $M$ are ____.

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