
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
Consider a circular cone with vertex \( V \), and let \( ABC \) be a triangle inscribed in the base of the cone, such that \( AB \) is a diameter and \( AC = BC \). Let \( L \) be a point on \( BV \) such that the volume of the cone is 4 times the volume of the tetrahedron \( ABCL \). Find the value of \( \frac{BL}{LV} \).

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