
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 positive integer \( x \) is called a magic number if, when \( x \) is expressed in binary form, it possesses an even number of '1's. For example, the first five magic numbers are \( 3, 5, 6, 9, \) and \( 10 \). Find, in decimal notation, the sum of the first 2003 magic numbers.

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