
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 following inequalities.<br/>$(1)\frac{{2x-1}}{3}-\frac{{9x+2}}{6}≤1$;<br/>$(2)\left\{{\begin{array}{l}{x-3(x-2)≥4}\\{\frac{{2x-1}}{5}＜\frac{{x+1}}{2}}\end{array}}\right.$.

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