
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
The graphs of $y=\log_3 x, y=\log_x 3, y=\log_{\frac{1}{2}} x,$ and $y=\log_x \frac{1}{2}$ are plotted on the same set of axes. Determine how many points in the plane with positive $x$-coordinates lie on two or more of these graphs.
A) 2  
B) 3  
C) 4  
D) 5  
E) 6

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