
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 $xOy$, the parametric equations of line $l$ are $$\begin{cases} x=-2+ \frac {1}{2}t \\ y= \frac { \sqrt {3}}{2}t\end{cases}$$, where $t$ is a parameter. A circle $C$ has the polar equation $ρ= \sqrt {10}$ in the polar coordinate system established with the origin as the pole and the positive semi-axis of $x$ as the polar axis.

(1) If line $l$ intersects circle $C$ at points $A$ and $B$, and point $P$ has coordinates $(-2,0)$, find $|PA|•|PB|$.
(2) Circle $M$ has its center on the polar axis and passes through the pole. If the length of the chord intercepted by line $l$ on circle $M$ is $1$, find the radius of circle $M$.

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