
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
There are 167 distinct cards with the numbers \(1, 3, 11, 3^{2}, 11^{2}, \ldots, 3^{83}, 11^{83}\) (each card has exactly one number, each number appears exactly once). In how many ways can 3 cards be chosen such that the product of the numbers on the chosen cards is the square of an integer divisible by 33?

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