
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 an angle $\alpha =1200^{\circ}$.  
$(1)$ Rewrite $\alpha$ as $\beta +2k\pi (k\in Z,0\leqslant \beta\ \ \lt 2\pi )$ and indicate in which quadrant the angle $\alpha$ lies;  
$(2)$ Find angles that have the same terminal side as $\alpha$ within the interval $\left[-2\pi ,2\pi \right]$.

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