
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
Given a sequence \(\{a_n\}\) where each term is either 1 or 0, the first term is 1, and between the \(k\)th 1 and the \((k+1)\)th 1, there are \(2k-1\) zeros, determine the position of the 2004th 1 in the sequence.

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