
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
$(1)$ Solve the inequality and write down the smallest integer solution: $5x+15 \gt x-1$;<br/>$(2)$ Solve the system of inequalities: $\left\{{\begin{array}{l}{-3(x-2)≥4-x①}\\{\frac{{1+4x}}{3}＞x-1②}\end{array}}\right.$.

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