
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 \( n \in \mathbb{N} \) and \( a \in [0, n] \), under the condition
$$
\sum_{i=1}^{n} \sin ^{2} x_{i}=a
$$
find the maximum value of \( \left| \sum_{i=1}^{n} \sin 2 x_{i} \right| \).

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