
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 quadratic function $f(x)=ax^{2}+(a-1)x+a$.
(1) If $a=2$, find the maximum value of the function $f(x)$ on the interval $[-1,1]$;
(2) Find the range of the real number $a$ such that the inequality $\frac{f(x)}{x}\geqslant 2$ holds for $x\in[1,2]$.

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