
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 207 different cards with numbers $1, 2, 3, 2^{2}, 3^{2}, \ldots, 2^{103}, 3^{103}$ (each card has one number, and each number appears exactly once). How many ways can you choose 3 cards such that the product of the numbers on the selected cards is a square of an integer that is divisible by 6?

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