
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 the parabola $C$: $y^{2}=2px(p > 0)$ with focus $F$, the distance from a point $P$ on the parabola to the $y$-axis is equal to $|PF|-1$.  
$(1)$ Find the value of $p$;  
$(2)$ Is there a positive number $m$, such that for any line passing through point $M(m,0)$ and intersecting the parabola $C$ at two points $A$ and $B$, it always holds that $\overrightarrow{FA} \cdot \overrightarrow{FB} < 0$? If it exists, find the range of $m$; if not, explain why.

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