
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 deck of three-colored cards has a total of 32 cards. Each color (red, yellow, and blue) has 10 cards numbered from $1$ to $10$. There are also two jokers (one big joker and one small joker), both numbered $0$. Any number of cards can be drawn from the deck, and the score for each card numbered $k$ is $2^{k}$ points. If the sum of scores of the drawn cards is 2004, such a set of cards is called a "good" set of cards. Find the number of "good" sets of cards.
(2004 China Girls Math Olympiad)

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