
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
From the five numbers -1, 0, 1, 3, and 4, randomly select one number and denote it as $a$. The probability that the hyperbola $y=\frac{7-3a}{x}$ lies in the first and third quadrants, and the system of inequalities $\begin{cases} 2x+3>9 \\ x-a<0 \end{cases}$ has no solution is _______.

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