
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
The function $sgn(x)$ is defined as follows:
$$
sgn(x)=
\begin{cases}
-1, & x < 0\\
0, & x = 0\\
1, & x > 0
\end{cases}
$$
Let $a = \frac{1}{\log_{\frac{1}{4}}\frac{1}{2015}} + \frac{1}{\log_{\frac{1}{504}}\frac{1}{2015}}$ and $b = 2017$. Determine the value of $\frac{a + b + (a - b)sgn(a - b)}{2}$.

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