
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 sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... is arranged in such a way that the first two numbers are 1, and starting from the third number, each number is the sum of the two numbers before it. This sequence is called the Fibonacci sequence. How many even numbers are there in the first 2004 numbers of the Fibonacci sequence?

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