
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
Are the vectors $c_{1}$ and $c_{2}$, constructed from the vectors $a$ and $b$, collinear?

Given:

$a=\{1; 4; -2\}$

$b=\{1; 1; -1\}$

$c_{1}=a+b$

$c_{2}=4a+2b$

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