
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
Each person in Cambridge drinks a (possibly different)  $12$  ounce mixture of water and apple juice,
where each drink has a positive amount of both liquids. Marc McGovern, the mayor of Cambridge, drinks  $\frac{1}{6}$  of the total amount of water drunk and  $\frac{1}{8}$  of the total amount of apple juice drunk. How many people are in Cambridge?



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