
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
The sum
$$
\frac{1}{1 \times 2 \times 3}+\frac{1}{2 \times 3 \times 4}+\frac{1}{3 \times 4 \times 5}+\cdots+\frac{1}{100 \times 101 \times 102}
$$
can be expressed as $\frac{a}{b}$, a fraction in its simplest form. Find $a+b$.

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