
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:<br/>$(1)$ Solve the equation: $\frac{2x}{x-2}+\frac{3}{2-x}=1$.<br/>$(2)$ Solve the system of inequalities: $\left\{\begin{array}{l}{2x-1≥3(x-1)}\\{\frac{5-x}{2}＜x+3}\end{array}\right.$.

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