
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 the sequence $\{a_{n}\}$ is a geometric sequence, if $a_{2}=1, a_{5}=\frac{1}{8}$, calculate the range of the value for $a_{1}a_{2}+a_{2}a_{3}+...+a_{n}a_{n+1} (n∈N^{*})$.

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