
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
Two identical rectangular containers are filled with spherical balls, each of radius 5 cm. A side view of the first four layers of each of the two different methods of packing is shown below. The first method (Container A) stacks the balls directly on top of each other in columns. The second method (Container B) arranges the balls in a hexagonal close packing.

After the containers have been packed with 100 balls each, what is the positive difference in the total heights (in cm) of the two packings?

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