
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 puppy, two cats, and a rabbit together weigh 40 pounds. The sum of the squares of the weights of the puppy and the larger cat is four times the weight of the smaller cat, and the sum of the squares of the weights of the puppy and the smaller cat equals the square of the weight of the larger cat. How much does the puppy weigh?

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