
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
Find the number of real solutions to the equation
\[
\frac{2}{x - 1} + \frac{4}{x - 2} + \frac{6}{x - 3} + \dots + \frac{200}{x - 100} = x.
\]

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