
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 container has a base radius of \(1 \text{ cm}\) and contains four solid iron spheres, each with a radius of \(\frac{1}{2} \text{ cm}\). The four spheres are in contact with each other, with the two at the bottom also in contact with the base of the container. Water is poured into the container until the water surface just covers all the iron spheres. How many cubic centimeters (\(\text{cm}^3\)) of water are needed?

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