
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 $\mathbf{a}$ and $\mathbf{b}$ are two unit vectors with an angle of $\frac{\pi}{4}$ between them, compute the volume of the parallelepiped formed by $\mathbf{a},$ $\mathbf{b} - \mathbf{a} \times \mathbf{b},$ and $\mathbf{b}.$

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