
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 contains 32 cards in total, with 10 cards of each color (red, yellow, blue), numbered 1 to 10. Additionally, there are one big joker and one small joker, each numbered 0. From this deck, some cards are drawn. Each card numbered \(k\) is worth \(2^k\) points. If the sum of the points of these drawn cards is 2004, the set of cards is called a "good" set. Determine the number of "good" sets.

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