
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 the line \[
\begin{cases} 
x=1+ \frac {1}{2}t \\
y=-3 \sqrt {3}+ \frac { \sqrt {3}}{2}t
\end{cases}
\] (where $t$ is a parameter) and the circle $x^{2}+y^{2}=R^{2}$ intersect at points $A$ and $B$, find the coordinates of the midpoint of segment $AB$.

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