
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 cylindrical vessel has a base radius of \( R = 4 \) cm. A sphere with radius \( r = 3 \) cm is placed inside the vessel. Water is then added to the vessel such that its free surface touches the surface of the sphere (the sphere does not float). Determine the thickness of the water layer that will result if the sphere is removed from the vessel.

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