
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
Reading material: In class, the teacher explained the following two problems on the blackboard:

Problem 1: Calculate: $77.7\times 11-77.7\times 5+77.7\times 4$.
Solution: $77.7\times 11-77.7\times 5+77.7\times 4=77.7\times \left(11-5+4\right)=777$.
This problem uses the distributive property of multiplication.
Problem 2: Calculate $(\frac{1}{2}×\frac{3}{2})×(\frac{2}{3}×\frac{4}{3})×(\frac{3}{4}×\frac{5}{4})\times …×(\frac{18}{19}×\frac{20}{19})$.
Solution: The original expression $=\frac{1}{2}×(\frac{3}{2}×\frac{2}{3})×(\frac{4}{3}×\frac{3}{4})×…×(\frac{19}{18}×\frac{18}{19})×\frac{20}{19}=\frac{1}{2}×\frac{20}{19}=\frac{10}{19}$.
This problem uses the commutative and associative properties of multiplication.

Attempt to solve: (1) Calculate: $99\times 118\frac{4}{5}+99×(-\frac{1}{5})-99×18\frac{3}{5}$.
Application of solution: (2) Subtract $\frac{1}{2}$ from $24$, then subtract $\frac{1}{3}$ from the remaining, then subtract $\frac{1}{4}$ from the remaining, and so on, until subtracting the remaining $\frac{1}{24}$. What is the final result?
(3) Given a rational number $a\neq 1$, calling $\frac{1}{1-a}$ the reciprocal difference of $a$, such as the reciprocal difference of $a=2$ is $\frac{1}{1-2}=-1$, the reciprocal difference of $-1$ is $\frac{1}{1-(-1)}=\frac{1}{2}$. If $a_{1}=-2$, $a_{1}$'s reciprocal difference is $a_{2}$, $a_{2}$'s reciprocal difference is $a_{3}$, $a_{3}$'s reciprocal difference is $a_{4}$, and so on. Find the value of $a_{1}+a_{2}+a_{3}-2a_{4}-2a_{5}-2a_{6}+3a_{7}+3a_{8}+3a_{9}$.

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