
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 vectors $\overrightarrow{m}=\left(2\sin x,-1\right), \overrightarrow{n}=\left(\sin x- \sqrt{3}\cos x,-2\right) $, and function $f\left(x\right)=\left( \overrightarrow{m}- \overrightarrow{n}\right)· \overrightarrow{m}+t $.

(I) If $f\left(x\right) $ has three zero points in the interval $\left[- \frac{π}{2}, \frac{π}{2}\right] $, find the value of $t$;

(II) In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are respectively $a$, $b$, $c$, $a=4$, the area of $\triangle ABC$ is $S= \sqrt{3} $, if $f\left(A\right)=2 $ and $t=0$, find the value of $b+c$.

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