
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
Observing the equations:<br/>$1\times 3+1=4=2^{2}$;<br/>$2\times 4+1=9=3^{2}$;<br/>$3\times 5+1=16=4^{2}$;<br/>$4\times 6+1=25=5^{2}$;<br/>$\ldots $<br/>$(1)7\times 9+1=( $______)$^{2}$;<br/>$(2)$ Using the pattern you discovered, calculate: $(1+\frac{1}{1×3})×(1+\frac{1}{2×4})×(1+\frac{1}{3×5})×⋅⋅⋅×(1+\frac{1}{198×200})$.

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