
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 equations \( y = \log_4 x \), \( y = \log_x 4 \), \( y = \log_{\frac{1}{4}} x \), and \( y = \log_x \frac{1}{4} \) plotted on the same set of axes. Determine the number of distinct points in the plane, with positive \( x \)-coordinates, at which at least two of these graphs intersect.
A) 2
B) 3
C) 4
D) 5
E) 6

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