
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
Solve the system of equations and inequalities:<br/>$(1)\left\{\begin{array}{l}{6x-2y=1}\\{2x+y=2}\end{array}\right.$；<br/>$(2)\left\{\begin{array}{l}{2x-10＜0}\\{\frac{x+1}{3}＜x-1}\end{array}\right.$.

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