
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 now has two identical basil plants, an aloe plant, and a cactus plant. She also has three different types of lamps: two identical white lamps, two identical red lamps, and one blue lamp. Each plant must be placed under exactly one lamp, but it's possible to put more than one plant under a lamp. How many ways are there for Rachel to arrange her plants under the lamps?

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