
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
Calculate the following:<br/>$(1)$ Solve the inequality: $x-\left(3x-1\right)\leqslant 2x+3$<br/>$(2)$ Solve the system of inequalities: $\left\{\begin{array}{c}3(x-1)＜4x-2\\ \frac{1+4x}{3}＞x-1\end{array}\right.$

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