
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
Alice has three daughters, each of whom has two daughters, each of Alice's six grand-daughters has one daughter. How many sets of women from the family of  $16$  can be chosen such that no woman and her daughter are both in the set? (Include the empty set as a possible set.)

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