
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
A mother purchases 6 blue plates, 3 red plates, 1 green plate, and 2 yellow plates. How many ways are there for her to arrange these plates for dinner around her circular table if she wants exactly one yellow plate to be next to the green plate?

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