
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 $\{a_n\}$ satisfies $\frac{\sin^2 a_6 \cos^2 a_9 - \sin^2 a_9 \cos^2 a_6}{\sin(a_7 + a_8)} = 1$, and the common difference $d \in (-1,0)$, determine the range of the first term $a_1$ of this sequence.

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