
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 the sequence \\(\{a_n\}\\) satisfying \\(\dfrac{{\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 \left({a_4}+{a_5}\right)}=1 \\), and the common difference \\(d \in (-1,0) \\), find the range of the first term \\(a_1\\).

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