
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
Let the function $f(x)$ have the domain $D$. If there exists a positive real number $k$ such that for any $x \in D$, $x+k \in D$ and $f(x+k) > f(x)$ always holds, then the function $f(x)$ is called a "$k$-type increasing function" on $D$. It is known that $f(x)$ is an odd function defined on $\mathbb{R}$ and when $x > 0$, $f(x) = |x-a| - 2a$. If $f(x)$ is a "$2017$-type increasing function" on $\mathbb{R}$, then the range of the real number $a$ is \_\_\_\_\_\_.

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