
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
Shrink the abscissa of all points on the graph of $f(x)=\sin (x+\frac{π}{3})$ to half of its original length, keeping the ordinate unchanged, to obtain the graph of a new function $y=g(x)$. Given that $g(x_{1})\cdot g(x_{2})=-1$ for $x_{1}\neq x_{2}$, find the minimum value of $|\frac{{x}_{1}+{x}_{2}}{2}|$.

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