
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 an arithmetic sequence $\{a_{n}\}$ with a common difference $d \in (0, 1)$, and $\frac{\sin^{2} a_{8} - \sin^{2} a_{4}}{\sin(a_{4} + a_{8})} = 1$. When $n=8$, the sum of the first $n$ terms of the sequence $S_{n}$ reaches its minimum value. Find the range of values for $a_{1}$.

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