
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 and two identical aloe plants. She also possesses three identical white lamps and three identical red lamps. She wants to arrange each plant under exactly one lamp (plants can share lamps, but must be under at least one). How many different ways can Rachel arrange these plants under her lamps?

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