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

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