
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 hyperbola $M$: $\dfrac {x^{2}}{9}- \dfrac {y^{2}}{7}=1$ has one of its foci as the focus $F$ of the parabola $N$: $y^{2}=2px(p > 0)$.  
$(1)$ Find the standard equation of the parabola $N$;  
$(2)$ Let the left and right vertices of the hyperbola $M$ be $C$, $D$, respectively. A line passing through $F$ and perpendicular to the $x$-axis intersects the parabola at points $A$, $B$. Find the value of $\overrightarrow{AC} \cdot \overrightarrow{BD}$.

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