
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:
\[ a = \{-1, 4, 2\} \]

\[ b = \{3, -2, 6\} \]

\[ c_1 = 2a - b \]

\[ c_2 = 3b - 6a \]

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