
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
To further enrich the cultural life of the citizens, the Cultural Bureau of a city plans to renovate the "Changhong" cinema and theater in the city, changing the original 1000 seats to 2004 seats as a gift for the New Year's Day of 2004. After the renovation, starting from the second row, each row has one more seat than the previous row, and the number of rows must be more than 20. How many design schemes are there, and how should it be designed?

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