
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
A bucket when one-third full of water weighs $c$ kilograms, and when it's three-quarters full, it weighs $d$ kilograms. Determine the total weight of the bucket when it is completely full of water, in terms of $c$ and $d$.
A) $\frac{8d - 3c}{5}$
B) $\frac{7c - 2d}{5}$
C) $\frac{9c - 4d}{5}$
D) $\frac{6c + 2d}{5}$
E) $\frac{-3c + 8d}{5}$

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