
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 sphere is inscribed in an equilateral cone, and a tangent plane parallel to the base of the cone is drawn at the point of contact. A sphere is then inscribed in the resulting smaller cone, and this process is repeated indefinitely. Determine the sum of the volumes of all the spheres if the slant height of the cone is $l = 2$.

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