
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 class, there are two (small) Christmas trees and five children. The teachers want to divide the children into two groups to form a ring around each tree, with at least one child in each group. The teachers distinguish the children but do not distinguish the trees: two configurations are considered identical if one can be converted into the other by swapping the trees (along with the corresponding groups) or by rotating each group around its tree. In how many ways can the children be divided into groups?

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