
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
In a cylindrical container with a base radius of $1 \mathrm{~cm}$, there are four solid iron balls each with a radius of $\frac{1}{2} \mathrm{~cm}$. These four balls are tangent to each other in pairs, with the two balls on the bottom layer being tangent to the container's base. Water is then poured into the container to just cover all the iron balls. How many $\mathrm{cm}^{3}$ of water are needed?

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