
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
Given a function $f(x) = x^2 + bx + c$ satisfies $f(2-x) = f(2+x)$, and given $f(0) > 0$, and $f(m) = f(n) = 0$ ($m \neq n$), find the value of $\log_{4}{m} - \log_{\frac{1}{4}}{n}$.

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