
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 inequalities:<br/>$(1)$ Solve the inequality: $1-\frac{x-3}{6}>\frac{x}{3}$;<br/>$(2)$ Solve the system of inequalities: $\left\{\begin{array}{l}{x+1\geq 3(x-3)}\\{\frac{x+2}{3}-\frac{x-1}{4}>1}\end{array}\right.$.

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