
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
An equilateral cone is immersed in water with its base downwards. The circle in which the water surface touches the cone has an area that is one-third of the base area of the cone, and the angle that the water surface makes with the side of the cone is $120^{\circ}$. What is the specific gravity of the material of the cone?

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