
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
Given the curve $y=x+1$, the vertical axis and the line $y=2$ form the closed region $D$, and the region $E$ is determined by the inequality system $\begin{cases} & -1 \leqslant x \leqslant 1 \\ & 0 \leqslant y \leqslant 2 \end{cases}$. Calculate the probability that a point randomly taken in region $E$ is precisely in region $D$.

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