
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
Let  $ f(x)\equal{}x^2\plus{}3$  and  $ y\equal{}g(x)$  be the equation of the line with the slope  $ a$ , which pass through the point  $ (0,\ f(0))$  .
Find the maximum and minimum values of  $ I(a)\equal{}3\int_{\minus{}1}^1 |f(x)\minus{}g(x)|\ dx$ .

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