
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  $y=f(x)$  be a function of the graph of broken line connected by points  $(-1,\ 0),\ (0,\ 1),\ (1,\ 4)$  in the  $x$  - $y$  plane.
Find the minimum value of  $\int_{-1}^1 \{f(x)-(a|x|+b)\}^2dx.$ *2010 Tohoku University entrance exam/Economics, 2nd exam*

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