
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 $y=f\left(x\right)$ is an odd function, where $f\left(x\right)=\cos \left(2x+\theta \right)$, with $\theta \in \left(0,\pi \right)$.  
$(1)$ Find the minimum positive period of the function $y=f\left(x\right)$ and the expression of $f\left(x\right)$;  
$(2)$ If $f({\frac{α}{2}})=-\frac{4}{5}$, where $\alpha \in (\frac{π}{2}$, $\pi )$, find the value of $\sin (\alpha +\frac{π}{3})$.

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