
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 three identical basil plants and two identical aloe plants. She also has three identical white lamps and three identical red lamps. Each plant must be under exactly one lamp, and more than one plant can be under the same lamp. How many ways are there for Rachel to arrange her plants under her lamps?

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