
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
In a certain measurement, the angle of elevation of point $B$ in the same plane as point $A$ was measured to be $50^{\circ}$, with a distance of $2$ to $A$. The angle of depression of point $C$ was measured to be $70^{\circ}$, with a distance of $3$ to $A$. Calculate the distance between $B$ and $C$.

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