
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 **u**, **v**, and **w** be unit vectors such that **u** · **v** = **u** · **w** = 0, and the angle between **v** and **w** is $\frac{\pi}{3}$. Then
\[
\mathbf{u} = m (\mathbf{v} \times \mathbf{w})
\]
for some constant **m**. Determine all possible values of **m**.

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