
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 $\vec{a}$ and $\vec{b}$ is $\theta$, we call $\vec{a} \times \vec{b}$ the "cross product" of vectors $\vec{a}$ and $\vec{b}$. $\vec{a} \times \vec{b}$ is a vector, and its length $\left|\vec{a} \times \vec{b}\right| = \left|\vec{a}\right|\left|\vec{b}\right|\sin \theta$. If $\left|\vec{a}\right|=4$, $\left|\vec{b}\right|=3$, and $\vec{a} \cdot \vec{b}=-2$, then $\left|\vec{a} \times \vec{b}\right|=$ ________.

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