
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
Given two jars of different volumes contain alcohol-water mixtures with the first jar having a ratio of alcohol to water of $p:1$ with total volume $V$, and the second jar having a ratio of $q:1$ with total volume $2V$. What is the ratio of the volume of alcohol to the volume of water in the resulting mixture after the contents of both jars are mixed together?

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