
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
Let the arithmetic sequence $\{a_{n}\}$ satisfy: $\frac{{{{\sin}^2}{a_3}-{{\cos}^2}{a_3}+{{\cos}^2}{a_3}{{\cos}^2}{a_6}-{{\sin}^2}{a_3}{{\sin}^2}{a_6}}}{{\sin({a_2}+{a_7})}}=1$, where the common difference $d\in \left(-1,0\right)$. Determine the range of the initial term $a_{1}$.

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