
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 whose terms are either 1 or 2, with the first term being 1, and between the $k$-th 1 and the $(k+1)$-th 1, there are $2^{k-1}$ 2s, i.e., 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, …, then the sum of the first 2010 terms of this sequence, $s_{2010}$, is.

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