
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
Let the function $f(x)= \frac {1}{3}x^{3}- \frac {a}{2}x^{2}+bx+c$, and the equation of the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$ is $y=1$.  
$(1)$ Find the values of $b$ and $c$;  
$(2)$ If $a > 0$, determine the intervals of monotonicity for the function $f(x)$;  
$(3)$ Let the function $g(x)=f(x)+2x$, and $g(x)$ has a decreasing interval in $(-2,-1)$, find the range of the real number $a$.

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