
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
There are three points \( (1, 0, a), (b, 1, 0), (0, c, 1) \) and a fourth point \( (4d, 2d, -2d) \) where \( a, b, c, \) and \( d \) are real numbers. Determine all possible values of \( d \) so that these points are collinear.

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