
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
If the graph of the function $y=f(x)$ is a polyline segment $ABC$, where $A(0,0)$, $B(1,1)$, and $C(2,0)$, then the area of the shape formed by the graph of the function $y=x\cdot f(x)$ $(0 \leqslant x \leqslant 2)$ and the $x$-axis is ______.

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