
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 \(b_1, b_2, \ldots\) of non-negative integers is defined by the rule \(b_{n+2} = |b_{n+1} - b_n|\) for \(n \geq 1\). If \(b_1 = 1001\), \(b_2 < 1001\), and \(b_{2010} = 1\), how many different values of \(b_2\) are possible?

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