
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 sequence of 1s and 2s is arranged in a row: 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, …, following a specific rule: the first number is 1, the second number is 2, the third number is 1. Generally, a row of 1s is written first, and then k 2s are inserted between the k-th and (k+1)-th 1s (where k=1, 2, 3, …). The questions are: (1) Is the 2007th number a 1 or a 2? (2) What is the sum of the first 2007 numbers?

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