
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 that the area of triangle ABC is $\frac{\sqrt{3}}{2}$, and $\overrightarrow {AB}\cdot \overrightarrow {AC}=-1$.

(1) Find the measure of angle $A$ and the minimum length of $BC$.

(2) Let $M$ be the midpoint of $BC$ such that $AM=\frac{\sqrt{3}}{2}$. The angle bisector of $\angle BAC$ intersects $BC$ at point $N$. Find the length of segment $MN$.

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