
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 cake shop sells $6$ different types of cakes and $4$ different types of cookies. Charlie and Delta decide to purchase some items. Charlie will not purchase more than $1$ of the same type due to dietary restrictions. Delta, on the other hand, focuses solely on cookies and might buy multiples of the same type. How many ways could they have left the store with $4$ products collectively? (A possible purchase scenario is Charlie buys $1$ piece of chocolate cake and $1$ piece of red velvet cookie while Delta buys $2$ oatmeal cookies.)

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