
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
A cone-shaped mountain has its base on the ocean floor and has a total height of 10000 feet. The top $\frac{2}{5}$ of the volume of the mountain is above water. If the radius of the mountain at the ocean floor is 2000 feet, determine the depth of the ocean at the base of the mountain in feet.

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