
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
The area of the parallelogram produced by vectors $\mathbf{a}$ and $\mathbf{b}$ is 12. Determine the area of the parallelogram formed by the vectors $3\mathbf{a} - \mathbf{b}$ and $4\mathbf{b} - 2\mathbf{a}.$

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