
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
Rotate the curves 

$$
y = -x^2 + 4
$$

and 

$$
16x^2 + 25y^2 = 400
$$

around the $Y$-axis. What is the volume of the region carved out by the solid of revolution of curve (1) from the solid of revolution of curve (2)?

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