
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 five cards with numbers $-3$, $-2$, $-1$, $1$, and $2$ respectively on the front side. Other than the numbers, all the cards are identical. After turning them over with the back side facing up, they are shuffled and one card is randomly drawn. Let $a$ be the number on the card. The probability that the graph of the quadratic function $y=x^2-(a^2+1)x+2-a$ does not pass through the point $(1,0)$, where $x$ is the independent variable, is <u>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</u>.

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