
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
The line  $ y\equal{}mx$  has 3 intersection points with the curve  $ y\equal{}|x(x\minus{}1)|$ . Find the value of  $ m$  such that the area of the 2 regions bounded by the line and the curve are equal.

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