
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 contain alcohol solutions. The first jar's volume is $3V$, with a ratio of alcohol to water of $p : 1$. The second jar's volume is $V$, with a ratio of alcohol to water of $q : 1$. When the contents of the two jars are mixed together, find the ratio of the volume of alcohol to the volume of water in the mixture.
A) $\frac{3p + q}{4}$
B) $\frac{3p(q+1) + q(p+1)}{3(q+1) + p+1}$
C) $\frac{4pq}{p+3q}$
D) $\frac{3(p+1) + q+1}{4}$

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