
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:

\[ a = \{-1, 3, 4\} \]
\[ b = \{2, -1, 0\} \]
\[ c_{1} = 6a - 2b \]
\[ c_{2} = b - 3a \]

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