
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
For \( r=1,2,3, \ldots \), let \( u_r = 1 + 2 + 3 + \ldots + r \). Find the value of
\[
\frac{1}{\left(\frac{1}{u_1}\right)} + \frac{2}{\left(\frac{1}{u_1} + \frac{1}{u_2}\right)} + \frac{3}{\left(\frac{1}{u_1} + \frac{1}{u_2} + \frac{1}{u_3}\right)} + \cdots + \frac{100}{\left(\frac{1}{u_1} + \frac{1}{u_2} + \cdots + \frac{1}{u_{100}}\right)}
\]

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