
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
Alloy $A$ of two metals has a mass of 6 kg, with the first metal being twice as abundant as the second metal. When placed in a container of water, it exerts a force of $30\ \mathrm{N}$ on the bottom. Alloy $B$ of the same metals has a mass of 3 kg, with the first metal being five times less abundant than the second metal. When placed in a container of water, it exerts a force of $10\ \mathrm{N}$ on the bottom. What force (in newtons) will the third alloy, obtained by combining the original alloys, exert on the bottom?

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