
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 volume of the parallelepiped determined by the vectors $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ is 3. Find the volume of the parallelepiped determined by the vectors $2\mathbf{a} - \mathbf{b}, 4\mathbf{b} + 5\mathbf{c},$ and $3\mathbf{c} + 2\mathbf{a}$.

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