
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
Let  $ K$  be the curved surface obtained by rotating the parabola  $ y \equal{} \frac {3}{4} \minus{} x^2$  about the  $ y$ -axis.Cut  $ K$  by the plane  $ H$  passing through the origin and forming angle  $ 45^\circ$  for the axis. Find the volume of the solid surrounded by  $ K$  and  $ H.$   

Note that you are not allowed to use Double Integral for the problem.

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