
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 pastry chef plans a week of desserts starting on Sunday through Saturday. Each day's dessert could be cake, pie, ice cream, or pudding, and no dessert is to be served on consecutive days. Additionally, there must be cake on Friday and at least three different types of desserts served throughout the week. How many different dessert menus for the week are possible?
**A)** 187
**B)** 324
**C)** 504
**D)** 729
**E)** 972

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