
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 the function $f(x)=x^{2}+4ax+2a+6$.
(1) If the minimum value of the function $f(x)=\log _{2} f(x)$ is $2$, find the value of $a$;
(2) If $f(x)\geqslant 0$ holds for any $x∈R$, find the range of the function $g(a)=2-a|a+3|$.

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