
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 {a<sub>n</sub>} that satisfies a<sub>n+1</sub>\=2(|a<sub>n</sub>|-1), n∈N*, if there exists a constant M>0 such that for any n∈N*, it always holds that |a<sub>n</sub>|≤M, then the range of values for a<sub>1</sub> is _____.

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