
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
If $\mathbf{c}$ and $\mathbf{d}$ are two unit vectors, with an angle of $\frac{\pi}{4}$ between them, then compute the volume of the parallelepiped generated by $\mathbf{c},$ $\mathbf{d} + 2\mathbf{d} \times \mathbf{c},$ and $\mathbf{d}.$

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