
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 5 cards with the numbers $-\frac{3}{2}$, $-1$, $0$, $1$, and $\frac{5}{4}$ written on the front respectively. Except for the numbers, all cards are identical. Turn them over with the back facing up, shuffle them, and randomly draw one card. Let $a$ be the number on the card. The probability that the linear function $y=(a-1)x+2$ with $x$ as the independent variable passes through the second and fourth quadrants, and the system of inequalities about $x$ $\left\{{\begin{array}{l}{x+1≤2a}\\{a-x≤2}\end{array}}\right.$ has a solution is ______.

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