
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
Consider the graphs of \(y = \log_5 x\), \(y = 3\log_x 5\), \(y = \log_{\frac{1}{5}} x\), and \(y = 5\log_x \frac{1}{5}\) 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) 3  
B) 4  
C) 6  
D) 5  
E) 7

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