
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
Lines $l_1$ and $l_2$ intersect at point $A$, with points $B$ and $C$ located on lines $l_1$ and $l_2$ respectively. If the angle between $\overrightarrow{AB}$ and $\overrightarrow{AC}$ is $60^{\circ}$, and $|\overrightarrow{AB}|=2$, $|\overrightarrow{AC}|=4$, calculate $|\overrightarrow{BC}|.$

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