
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 kindergarten, there are two small Christmas trees and five children. The teachers want to divide the children into two circles around each of the Christmas trees, with at least one child in each circle. The teachers can distinguish between the children but not between the trees: two such divisions into circles are considered the same if one can be obtained from the other by swapping the Christmas trees (along with the corresponding circles) and rotating each circle around its respective tree. How many ways can the children be divided into circles?

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