
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 $y=x^{2}$ and the line $y=1$, the region determined by the enclosed area formed by these two functions, $D$, and the region $E$ defined by the inequality system $\begin{cases} -1\leqslant x\leqslant 1 \\ 0\leqslant y\leqslant 1 \end{cases}$, find the probability that a randomly chosen point within region $E$ is also within region $D$.

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