
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 the angle between vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\theta$, then we call $\overrightarrow{a} \times \overrightarrow{b}$ the "vector product" of vectors $\overrightarrow{a}$ and $\overrightarrow{b}$. $\overrightarrow{a} \times \overrightarrow{b}$ is a vector, and its magnitude $|\overrightarrow{a} \times \overrightarrow{b}| = |\overrightarrow{a}||\overrightarrow{b}|\sin \theta|$. If $|\overrightarrow{a}| = 4$, $|\overrightarrow{b}| = 3$, and $\overrightarrow{a} \cdot \overrightarrow{b} = -2$, then $|\overrightarrow{a} \times \overrightarrow{b}| = $ ______.

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