
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
Given three vectors $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ in three-dimensional space such that the volume of the parallelepiped they form is 8, compute the volume of the parallelepiped formed by $\mathbf{2a} + \mathbf{b}$, $\mathbf{b} + 5\mathbf{c}$, and $2\mathbf{c} + 4\mathbf{a}$.

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