
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
Determine the probability that a point $P$ randomly selected within the plane region $N$ defined by the system of inequalities $\begin{cases} 0 \leq x \leq 1 \\ 0 \leq y \leq e \end{cases}$ also lies within the plane region $M$ defined by the system of inequalities $\begin{cases} x + y \geq 1 \\ e^x - y \geq 0 \\ 0 \leq x \leq 1 \end{cases}$.

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