
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 $\alpha=1690^\circ$,  
(1) Express $\alpha$ in the form of $2k\pi+\beta$ ($k\in \mathbb{Z}$, $\beta\in[0,2\pi)$).  
(2) Find $\theta$ such that $\theta$ has the same terminal side as $\alpha$, and $\theta\in(-4\pi,-2\pi)$.

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