
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 three identical cactus plants and one unique orchid plant. She also has three identical yellow lamps and two identical blue lamps to arrange these plants under. Each plant must be under exactly one lamp, and each lamp can have more than one plant under it. How many ways can Rachel arrange her plants under these lamps?

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