
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 $\alpha=2010^\circ$.
(1) Rewrite $\alpha$ in the form of $k\cdot360^\circ+\beta$ ($k\in\mathbb{Z}$, $0^\circ\leq\beta<360^\circ$) and indicate which quadrant the angle belongs to;
(2) Find $\theta$ such that $\theta$ has the same terminal side as $\alpha$, and $-360^\circ\leq\theta<720^\circ$.

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