
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/>$(1)-3\frac{1}{4}-(-\frac{1}{9})+(-\frac{3}{4})+1\frac{8}{9}$;<br/>$(2)(-50)×(2\frac{1}{5}-3\frac{3}{10}+1\frac{7}{25})$;<br/>$(3)(\frac{3}{5}-\frac{1}{2}-\frac{7}{12})×(60×\frac{3}{7}-60×\frac{1}{7}+60×\frac{5}{7})$;<br/>$(4)(-\frac{3}{2})^3×(-\frac{3}{5})^2-2\frac{5}{19}×\frac{19}{43}×(-1\frac{1}{2})^{3}+(\frac{4}{5})^{2}×(-\frac{3}{2})^{3}$;<br/>$(5)\frac{1}{1×2}+\frac{1}{2×3}+…+\frac{1}{49×50}$.

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