
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
Jia and Yi are solving an equation involving $x$: $\log_{2}x+b+c\log_{2}2=0$. Jia made a mistake with the constant $b$, leading to two solutions, $\frac{1}{4}$ and $\frac{1}{8}$. Yi made a mistake with the constant $c$, resulting in two solutions, $\frac{1}{2}$ and $64$. Find the true roots of this equation.

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