
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
Calculate:<br/>$(1)$ Solve the following system of linear equations:<br/>①$\left\{\begin{array}{l}{x=7y}\\{2x+y=30}\end{array}\right.$；<br/>②$\left\{\begin{array}{l}{\frac{x}{2}+\frac{y}{3}=7}\\{\frac{x}{3}-\frac{y}{4}=-1}\end{array}\right.$；<br/>$(2)$ Solve the following system of linear inequalities:<br/>①$4+3\left(x-1\right) \gt -5$；<br/>②$\left\{\begin{array}{l}{\frac{1}{2}(x-2)+3＞7}\\{-\frac{1}{3}(x+3)-4＞-10}\end{array}\right.$.

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