
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 $f(x)=ax^{2}-|x-1|+2a$ where $a\in R$.
1. Solve the inequality $f(x)\geqslant 0$ when $a= \dfrac {1}{2}$;
2. Find the range of $a$ that makes $f(x)\geqslant 0$ always true.

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