
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
If \( |x - \sin(\log y)| = x + \sin(\log y) \) where \( x \) and \( \sin(\log y) \) are real, then find the possible values of \( y \).
A) \(y = 1\) 
B) \(y = e^{\pi}\)
C) \(y = e^{2\pi}\)
D) All \( y = e^{2n\pi} \) for \( n \text{ integer} \)
E) None of these

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