
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
Two jars with different volumes (one with volume $V_1$ and the other $V_2$) are filled with alcohol solutions with different ratios. For the jar with volume $V_1$, the ratio of the volume of alcohol to the volume of water is $r:1$, and for the jar with volume $V_2$, the ratio is $s:1$. The entire contents of the two jars are mixed together. What is the ratio of the volume of alcohol to the volume of water in this mixture?
A) $\frac{r(s+1)V_1 + s(r+1)V_2}{(s+1)V_1 + (r+1)V_2}$
B) $\frac{r+s}{2}$
C) $\frac{rs}{r+s}$
D) $\frac{2rs}{r+s+1}$
E) $\frac{2(r+s)}{rs}$

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