
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
$(1)$ Calculate: $(-\frac{1}{3})^{-2}-2\sin30{}°+(\pi-2023){}°$.  
$(2)$ Solve the system of inequalities: $\left\{\begin{array}{l}{-x+1\geq 0}\\{\frac{2x+3}{5} > -1}\end{array}\right.$.

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