
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
In a nursery group, there are two small Christmas trees and five children. The caregivers want to split the children into two dance circles around each tree, with at least one child in each circle. The caregivers distinguish between the children but not between the trees: two such groupings are considered identical if one can be obtained from the other by swapping the trees (along with the corresponding circles) and rotating each circle around its tree. How many ways can the children be divided into dance circles?

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