
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 slant height of a cone is 17 cm, and the height from the vertex to the center of the base is 15 cm. Calculate both the volume and the lateral surface area of the cone, expressing your answers in terms of $\pi$.

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