
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
Cassandra and Joy decide to dine out at a restaurant that has 15 dishes on its menu. If each of them orders exactly one dish, and each dish can be ordered by both, but they also agree to share one appetizer from 5 additional options, how many different combinations of dishes can they order respecting all conditions?

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