
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 $f(x)$ is a quadratic function, and $f(-1)=2$, $f′(0)=0$, $\int_{0}^{1}f(x)dx=-2$.

1. Find the analytical expression of $f(x)$;
2. Find the maximum and minimum values of $f(x)$ on $[-1,1]$.

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