
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
Let $b_1=1$, for any $n\in\mathbb{N}^*$, we have $b_n>0$, and $nb_{n+1}^2-2b_n^2-(2n-1)b_{n+1}b_n=0$. Let $M(x)$ denote the units digit of the integer $x$, then $M(b_{2010})=\boxed{2}$.

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