
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
Two individuals, A and B, are solving an equation involving $x$: $\log_{2}x + b + c\log_{x}2 = 0$. A made a mistake with the constant $b$ and obtained two roots, $\frac{1}{4}$ and $\frac{1}{8}$. B made a mistake with the constant $c$ and obtained two roots, $\frac{1}{2}$ and $64$. Find the true roots of the equation.

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