
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/>$(1)64.83-5\frac{18}{19}+35.17-44\frac{1}{19}$;<br/>$(2)(+2.5)+(-3\frac{1}{3})-(-1)$;<br/>$(3)\frac{(0.125+\frac{3}{5})×\frac{33}{87}}{12.1×\frac{1}{11}$;<br/>$(4)41\frac{1}{3}×\frac{3}{4}+52\frac{1}{2}÷1\frac{1}{4}+63\frac{3}{5}×\frac{5}{6}$;<br/>$(5)3\frac{2}{3}×2\frac{2}{15}+5\frac{2}{3}×\frac{13}{15}-2×\frac{13}{15}$;<br/>$(6)\frac{567+345×566}{567×345+222}$;<br/>$(7)3\frac{1}{8}÷[(4\frac{5}{12}-3\frac{13}{24})×\frac{4}{7}+(3\frac{1}{18}-2\frac{7}{12})×1\frac{10}{17}]$;<br/>$(8)\frac{0.1×0.3×0.9+0.2×0.6×1.8+0.3×0.9×2.7}{0.1×0.2×0.4+0.2×0.4×0.8+0.3×0.6×1.2}$;<br/>$(9)\frac{1^2+2^2}{1×2}+\frac{2^2+3^2}{2×3}+\frac{3^2+4^2}{3×4}+…+\frac{2022^2+2023^2}{2022×2023}$.

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