
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 frustum-shaped glass full of water, with the lower and upper inner diameters being 4 and 14 units respectively, and an inner height of 12 units. First, a solid sphere A is placed at the bottom such that it touches the cup walls (i.e., it is tangent). Then, a second solid sphere B is placed such that it touches sphere A and also touches the cup walls. Find the volume of water in the cup.

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