
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
How many solutions does the equation 
\[
\frac{(x-1)(x-2)(x-3)\dotsm(x-200)}{(x-1^2)(x-2^2)(x-3^2)\dotsm(x-10^2)(x-11^3)(x-12^3)\dotsm(x-13^3)}
\]
have for \(x\)?

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