
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
There are three numbers: $2$, $1$, $-1$. Choose the appropriate method to find the probability of the following events:
1. Randomly select a number to be the value of $m$ in the function $y=(m-1)x^{2}+mx+1$, such that the graph of the resulting function has exactly one intersection point with the $x$-axis.
2. Successively select two different numbers as the values of $a$ and $b$, such that the point $P(a,b)$ lies on the graph of the parabola $y=-x^{2}+x+2$.

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