
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 vectors $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ is 6. Find the volume of the parallelepiped determined by $\mathbf{a} + 2\mathbf{b},$ $\mathbf{b} + \mathbf{c},$ and $2\mathbf{c} - 5\mathbf{a}.$

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