
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
Lucy places a total of 30 purple Easter eggs in some pink baskets and a total of 45 yellow Easter eggs in several brown baskets. Each basket contains the same number of eggs, and there are at least 5 eggs in each basket. How many eggs did Lucy put in each basket?

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