
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 $D$ be the determinant of the matrix whose column vectors are $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}.$  Find the determinant of the matrix whose column vectors are $2\mathbf{a} + 3\mathbf{b},$ $3\mathbf{b} + 4\mathbf{c},$ and $4\mathbf{c} + 2\mathbf{a},$ in terms of $D.$

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