
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 consists of 32 cards: 10 red, 10 yellow, and 10 blue cards, each numbered from 1 to 10, and two special cards called the Joker, each numbered 0. Draw any number of cards from this deck and calculate the total score according to the following rule: each card numbered \( k \) corresponds to \( 2^k \) points. If the sum of the points is 2004, the collection of these cards is called a "good hand." Determine the number of "good hands."

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