
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
Three points are given in the form $(1,0,a), (b,1,0),$ and $(0,c,1),$ where $a, b, c$ are real numbers. A fourth point is of the form $(8e, 8e, -e)$. Determine all possible values of $e$ such that these four points lie on a single straight line.

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