
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: $\left\{\begin{array}{l}\frac{x}{3}+\frac{y}{4}=4\\ 2x-3y=12\end{array}\right.$; <br/>$(2)$ Solve the system of inequalities: $\left\{\begin{array}{l}\frac{x}{3}>\frac{x-1}{2}\\ 3(x+2)\geq 2x+5\end{array}\right.$.

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