
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 measuring cup placed horizontally with a base radius of $\sqrt{3}$ cm, there is a certain amount of water. Now, a solid iron ball with a radius of $R$ cm is placed into the cup. The ball is completely submerged in the water without any water spilling out. If the water level rises exactly by $R$ cm, then $R = \_\_\_\_\_\_$ cm.

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