
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 $M$ is the solution set of the inequality $x^2+(a-4)x-(a+1)(2a-3)<0$, and one element in $M$ is $0$, find the range of the real number $a$ and express $M$ in terms of $a$.

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