
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
Let vector $\mathbf{a} = (1, -3)$, $\mathbf{b} = (-2, 4)$. If the directed line segments representing the vectors $4\mathbf{a}$, $3\mathbf{b} - 2\mathbf{a}$, and $\mathbf{c}$ can form a triangle when connected head-to-tail, find the vector $\mathbf{c}$.

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