
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
There is a sequence of spheres with radii forming a geometric sequence with first term $1$ and common ratio $\frac{1}{2}$. The volumes of these spheres are denoted as $V\_1$, $V\_2$, ..., $V\_n$, ... . Calculate the limit of the sum of these volumes as $n$ approaches infinity, i.e., $\lim_{n\to\infty}(V\_1+V\_2+...+V\_n)=$ ___.

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