
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 $b_1=1$, for any $n\in\mathbb{N}^*$, $b_n>0$, and $nb_{n+1}^2-2b_n^2-(2n-1)b_{n+1}b_n=0$. Find $\log_{2}b_{2010}$.

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