
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 a sequence $\{b_n\}$ satisfying $b_1=1$, $b_2=x$ ($x\in\mathbb{N}$), and $b_{n+1}=|b_n-b_{n-1}|$ ($n\geq2$, $n\in\mathbb{N}$). If there are exactly 30 terms equal to 0 among the first 100 terms, then the value of $x$ is.

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