
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
For the function $f(x)=- \frac {1}{3}x^{3}+2ax^{2}-3a^{2}x+b$ where $(0 < a < 1)$:
1. Determine the intervals of monotonicity for the function $f(x)$, and find the maximum and minimum values of the function $f(x)$;
2. If the inequality $|f'(x)|\leqslant a$ always holds when $x\in[a+1,a+2]$, find the range of values for the real number $a$.

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