
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
Square $EFGH$ has area $64$, and $\overline{EF}$ is parallel to the x-axis. Vertices $E,$ $F$, and $G$ are on the graphs of $y = \log_{b}x,$ $y = 3\log_{b}x,$ and $y = 5\log_{b}x,$ respectively. What is $b?$
A) $2^\frac{8}{7}$ 
B) $2^\frac{7}{8}$ 
C) $2^\frac{6}{7}$ 
D) $2^\frac{9}{8}$

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