
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 that the domain of the function $f(x)$ is $[1,+\infty)$, and $f(x)= \begin{cases} 1-|2x-3|, & 1\leqslant x < 2 \\ \frac {1}{2}f\left( \frac {1}{2}x\right), & x\geqslant 2 \end{cases}$, then the number of zeros of the function $y=2xf(x)-3$ in the interval $(1,2017)$ is ______.

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