
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 dump truck delivered sand to a construction site, forming a conical pile with a diameter of $10$ feet. Initially, the height of the pile was $60\%$ of its diameter. After some time, an additional $2$ cubic feet of sand was added to the pile, maintaining its conical shape but increasing the height. Calculate the new height of the sand pile. Express your answer in terms of $\pi$.

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