
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 that $a > 0$, the function $f(x)= \begin{cases} - \frac {1}{3}x^{3}+ \frac {1-a}{2}x^{2}+ax- \frac {4}{3},x\leqslant 1 \\ (a-1)\ln x+ \frac {1}{2}x^{2}-ax,x > 1\\ \end{cases}$ is monotonically increasing in the interval $(-a,2a)$. Determine the range of values for the real number $a$.

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