
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
The radii of the base circles of a truncated cone are $R$ and $r$ respectively, where $R > r$. Each base circle, with the center of the opposite circle as the vertex, forms a cone. The volume of the solid bounded by these two cone surfaces and the lateral surface of the given truncated cone is $k$. Calculate

a) the volume $K$ of the truncated cone,

b) the surface area $F$ of the lateral surface of the truncated cone, given $R$, $r$, and $k$.

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