
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 \\(\alpha = -1920^{\circ}\\)  
   \\((1)\\) Express \\(\alpha\\) in the form of \\(\beta + 2k\pi\\) \\((k \in \mathbb{Z}, 0 \leqslant \beta \leqslant 2\pi)\\) and indicate which quadrant the angle belongs to.  
   \\((2)\\) Find the angle \\(\theta\\) that has the same terminal side as \\(\alpha\\) and satisfies \\(-4\pi \leqslant \theta < 0\\).

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