
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 $f(x)=x^{2}-ax$ $(a∈R)$.
(1) If $a=2$, find the solution set of the inequality $f(x)\geqslant 3$.
(2) If $x∈[1,+∞)$, the inequality $f(x)\geqslant -x^{2}-2$ always holds. Find the range of values for $a$.

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