
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
Let \( y(x) \) be the unique solution of the differential equation
\[ \frac{\mathrm{d} y}{\mathrm{~d} x}=\log_{e} \frac{y}{x}, \]
where \( x > 0 \) and \( y > 0 \),
with the initial condition \( y(1) = 2018 \).
How many positive real numbers \( x \) satisfy the equation \( y(x) = 2000? \)

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