
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 inequalities
$(1)\begin{cases} 3x-(x-2)\geqslant 6 \\ x+1 > \frac {4x-1}{3}\end{cases}$

$(2)$ Find the positive integer solutions for the system of inequalities $\begin{cases} 2x+1 > 0 \\ x > 2x-5\end{cases}$

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