
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
When the bucket is three-quarters full of water, the weight of water in the bucket is $\frac{3}{4}w$, where $w$ is the weight of a full bucket. The weight of the bucket plus the water is given by the equation $p=r+\frac{3}{4}w$, and when the bucket is one-third full of water, the weight of water in the bucket is $\frac{1}{3}w$, and the total weight is given by $q=r+\frac{1}{3}w$. Express the weight of a full bucket in terms of p, q, and r.

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