
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 32 cards, consisting of 10 cards in each of red, yellow, and blue colors numbered from 1 to 10, plus one Joker and one extra Joker both numbered 0, is given. From this deck, a number of cards are drawn. The value of each card numbered $k$ is calculated as $2^{k}$. If the sum of the values of these cards equals 2004, these cards are considered a "good" set of cards. Find the number of "good" sets of cards.

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