
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 with a base radius of 1 cm contains four solid iron balls, each with a radius of 0.5 cm. The balls are arranged such that each pair of balls touches, and the two balls at the bottom also touch the base of the container. Water is poured into the container until it just covers all the iron balls. The volume of water needed is _______ cm<sup>3</sup>.

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