
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 consists of 32 cards in three colors: red, yellow, and blue. Each color has 10 cards numbered from 1 to 10, and there are also two jokers, each numbered 0. When selecting any number of cards from this deck, the score of each card numbered \( k \) is \( 2^k \) points. If the total score of selected cards is 2004, these cards form a "good" set. Determine the number of "good" sets.

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