
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 \(0 \leqslant x_{1} \leqslant x_{2}\), the sequence \(\left\{x_{n}\right\}\) satisfies
\[ x_{n+2} = x_{n+1} + x_{n} \quad (n \geqslant 1). \]

If \(1 \leqslant x_{7} \leqslant 2\), then the range of possible values for \(x_{8}\) is:

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