
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
(1) Evaluate  $ \int_{\minus{}\sqrt{3}}^{\sqrt{3}}( x^2\minus{}1)dx,\  \int_{\minus{}\sqrt{3}}^{\sqrt{3}} (x\minus{}1)^2dx,\  \int_{\minus{}\sqrt{3}}^{\sqrt{3}} (x\plus{}1)^2dx$ .

(2) If a linear function  $ f(x)$  satifies  $ \int_{\minus{}\sqrt{3}}^{\sqrt{3}} (x\minus{}1)f(x)dx\equal{}5\sqrt{3},\ \int_{\minus{}\sqrt{3}}^{\sqrt{3}} (x\plus{}1)f(x)dx\equal{}3\sqrt{3}$ , then we have  $ f(x)\equal{}\boxed{\ A\ }(x\minus{}1)\plus{}\boxed{\ B\ }(x\plus{}1)$ , thus we have  $ f(x)\equal{}\boxed{\  C\ }$ .

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