
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
Given the system of inequalities $$\begin{cases} \left.\begin{matrix}x^{2}-4x+3<0 \\ x^{2}-6x+8<0\end{matrix}\right.\end{cases},$$ the solution set is a subset of the solution set of the inequality $2x^{2}-9x+a<0$. The range of the real number $a$ is \_\_\_\_\_.

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