
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 that \(\left\{a_{n}\right\}\) is a geometric sequence, \(a_{2} = 2\), and \(a_{5}=\frac{1}{4}\), determine the range of values for \(a_{1} a_{2} + a_{2} a_{3} + \cdots + a_{n} a_{n+1}\) (where \(n \in \mathbf{N}^{*}\)).

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