
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 $\left\{\begin{array}{c}3a+2b=-26,\\ 2a-b=-22.\end{array}\right.$;  
$(2)$ Solve the inequality $\frac{5}{2}-\frac{4x-1}{3}≥\frac{2x+3}{2}+2$.

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