
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
$(1)$ Solve the system of equations $\left\{\begin{array}{l}{3(y-2)=x-1}\\{2(x-1)=5y-8}\end{array}\right.$; <br/>$(2)$ Solve the system of linear inequalities $\left\{\begin{array}{l}{3x≤2x+3}\\{\frac{x+1}{6}-1＜\frac{2x+2}{3}}\end{array}\right.$.

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