
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
Given a cone whose base radius and height are equal, and its lateral area is $4\sqrt{2}\pi$. A section is made through two generatrices of the cone, and the section is an equilateral triangle. The distance from the center of the base of the cone to the section is ______.

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