
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: The sequence $\{b_n\}$ satisfies $b_1=1$, $b_2=x$ ($x\in\mathbb{N}^*$), $b_{n+1}=|b_n-b_{n-1}|$ ($n\geq2$, $n\in\mathbb{N}^*$).

① If $x=2$, then the sum of the first 10 terms of the sequence is     ;  
② If exactly 30 of the first 100 terms are 0, then the value of $x$ is     .

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