
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
In the rectangular coordinate system $(x-O-y)$, the curve $(E)$ is given by the parametric equations: $\begin{cases} x=2\cos t\\ y=2\sin t \end{cases}$ $(t$ is the parameter$)$

(1) In the polar coordinate system $(O-x)$, if $A$, $B$, $C$ are three points on $(E)$ arranged counterclockwise, $\triangle ABC$ is an equilateral triangle, and the polar angle of point $A$ is $\theta= \frac {\pi}{4}$, find the polar coordinates of points $B$ and $C$.

(2) In the rectangular coordinate system $(x-O-y)$, the moving points $P$ and $Q$ are both on the curve $(E)$, with corresponding parameters $t=\alpha$ and $t=2\alpha$ $(\0 < \alpha < 2\pi)$, and $M$ is the midpoint of $PQ$. Find the range of values for $|MO|$.

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