
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
Rachel has two identical rose plants and an orchid. She has two identical blue lamps and two identical green lamps. Each plant must be under exactly one lamp, but more than one plant can be under a single lamp. How many ways can Rachel arrange her plants under these lamps?

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