
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
From a soap solution with a surface tension $\alpha$, we blow a bubble with a radius $r_{0}$. Then we charge the bubble to a potential $U$ by using an insulated tube (e.g., with a comb). What will the radius of the bubble be if we allow air to flow freely through the tube? (Given: $\alpha=4 \cdot 10^{-2} \mathrm{~N} / \mathrm{m}, r_{0}=2 \cdot 10^{-2} \mathrm{~m}, U=6,7 \cdot 10^{3} \mathrm{~V}$.)

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