
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 vectors \(a\) and \(b\), collinear?

Given:

\[ a = \{3, 4, -1\} \]

\[ b = \{2, -1, 1\} \]

\[ c_{1}=6a-3b \]

\[ c_{2}=b-2a \]

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