
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
At the 'Inept Hands' club, a makeshift lever scale was made with unequal arm lengths and containers of varying weights. As a result of four weighings on this scale, the following "equilibria" were obtained:

$$
\begin{array}{ll}
{[\text { left } 3 \text { kg }=\text { right melon]; }} & \text { [left melon }=\text { right 5.5 kg]; } \\
\text { [left } 5 \text { kg = right watermelon]; } & \text { [left watermelon }=\text { right } 10 \text { kg]. }
\end{array}
$$

What is the true weight (mass) of the melon and watermelon? (12 points)

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