
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 that the solution set of the inequality in terms of $x$, $\left(a-2\right)x^{2}+\left(2a-1\right)x+6 \gt 0$, is $M$. If $3\in M$ and $5\notin M$, then the range of real number $a$ is ______.

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