
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 $1 \text{ cm}$ contains four solid iron balls, each with a radius of $\frac{1}{2} \text{ cm}$. The four balls touch each other in pairs, and the two balls in the bottom layer touch the base of the container. Now, water is added to the container until the water surface just submerges all of the iron balls. How many $\text{cm}^{3}$ of water need to be added?

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