
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 a parallelepiped determined by vectors $\mathbf{u}$, $\mathbf{v}$, and $\mathbf{w}$ in three-dimensional space is 6. Find the volume of the parallelepiped determined by the vectors $2\mathbf{u} + 3\mathbf{v}$, $\mathbf{v} + 2\mathbf{w}$, and $\mathbf{w} + 5\mathbf{u}$.

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