
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 $\bold{v} = \begin{pmatrix} 3 \\ -4 \\ 2 \end{pmatrix}$ and $\bold{w} = \begin{pmatrix} -1 \\ 5 \\ 3 \end{pmatrix}$. Find the volume of the parallelepiped with vertices $\bold{0}$, $\bold{v}$, $\bold{w}$, $\bold{v} + \bold{w}$, $\bold{u}$, $\bold{v} + \bold{u}$, $\bold{w} + \bold{u}$, and $\bold{v} + \bold{w} + \bold{u}$, where $\bold{u} = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}$.

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