
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
The value of $$∫_{ -3 }^{ 3 }(\sqrt {9-x^{2}} - x^{3})dx$$ is \_\_\_\_\_\_, and if $f(x) = \frac {a^{2}}{x}$ ($a > 0$) has a derivative of -4 at $x = x_{0}$, then $x_{0}$ = \_\_\_\_\_\_.

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