
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 $f(x)=x^{2}+ax+2$, where $a\in\mathbb{R}$.
(1) If the solution set of the inequality $f(x)\leqslant 0$ is $[1,2]$, find the solution set of the inequality $f(x)\geqslant 1-x^{2}$.
(2) If the function $g(x)=f(x)+x^{2}+1$ has two distinct zeros in the interval $(1,2)$, find the range of values for the real number $a$.

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