
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 a line with parameter \( t \) specified by
\[
\begin{cases}
x = 1 + \dfrac{1}{2}t \\
y = -3 \sqrt{3} + \dfrac{\sqrt{3}}{2}t
\end{cases},
\]
and a circle given by \( x^{2} + y^{2} = 16 \), the line intersects the circle at points \( A \) and \( B \). Determine the coordinates of the midpoint of segment \( AB \).

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