
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
For any real numbers \(a_{1}, a_{2}, \cdots, a_{2016}\), find the range of values of
$$
\frac{7+23 \sum_{1 \leqslant i<j \leqslant 2} \sin ^{2}\left(a_{i}-a_{j}\right)}{7+24 \sum_{1 \leqslant i<j \leqslant 2} \cos ^{2}\left(a_{i}-a_{j}\right)}.
$$

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