
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
Given a right circular cone, a right circular cylinder, and a sphere which all have the same radius, but the common height of the cone and the cylinder is twice the radius of the sphere. If the volume of the cone is $A$, the volume of the cylinder is $M$, and the volume of the sphere is $C$, establish the correct relation among these volumes.
A) $2A + M = 2C$
B) $2A + M = 2.5C$
C) $A + 2M = 2.5C$
D) $2A + M = 3C$

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