
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
A function is defined as $f(x)= \frac {1}{3}x^{3}- \frac {a}{2}x^{2}+bx+c$. The tangent line to the curve $y=f(x)$ at the point $(0, f(0))$ is given by $y=1$. 
(1) Find the values of $b$ and $c$. 
(2) Let another function be $g(x)=f(x)+2x$. If $g(x)$ is monotonically increasing over $\mathbb{R}$, determine the range of real number $a$.

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