
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
A new definition: $\left[k,b\right]$ is a "double subtraction point" of a linear function $y=kx+b\left(k\neq 0\right)$. If $\left[3,a-2\right]$ is a "double subtraction point" of a certain proportional function $y=kx\left(k\neq 0\right)$, then the solution set of the inequality system about $y$ $\left\{\begin{array}{l}{2(y+1)<5y-7}\\{\frac{y+a}{2}<5}\end{array}\right.$ is ______.

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