
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
X is the set \(\{1, 2, 3, ... , n\}\). How many ordered 6-tuples \((A_1, A_2, ... , A_6)\) of subsets of X are there such that every element of X belongs to 0, 3, or 6 subsets in the 6-tuple?

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