
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
Janka and Hanka enjoy playing with animal models. Hanka built a rectangular pen for her cows out of bottle caps as shown in the picture. Janka made a pen for her sheep in the shape of an equilateral triangle using all of her bottle caps. She then took it apart and built a square pen for the sheep using all of her caps again. How many bottle caps could Janka have? Find at least 2 solutions.

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