
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 the function $f\left( x \right)=-{{x}^{3}}+3{{x}^{2}}+9x+a$, where $a$ is a constant.

1. Find the interval where the function $f\left( x \right)$ is strictly decreasing.
2. If the maximum value of $f\left( x \right)$ on the interval $\left[-2, 2 \right]$ is $20$, find the minimum value of $f\left( x \right)$ on this interval.

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