
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
The cards are numbered \( 1, 2, \cdots, 10 \); there are also one big and one small joker, both numbered 0. A set of cards is randomly drawn from this deck, and the score is calculated according to the following rule: each card numbered \( k \) is worth \( 2^k \) points. If the sum of these points equals 2004, the set of cards is called a "good" hand. Find the number of "good" hands.

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