
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 angle $\alpha=1200^\circ$  
(1) Rewrite $\alpha$ in the form of $\beta+2k\pi$ ($k\in\mathbb{Z}$, $0\leq\beta\leq2\pi$) and indicate in which quadrant angle $\alpha$ is;  
(2) Find the angle in the interval \[-4\pi, \pi\] that has the same terminal side as $\alpha$.

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