
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 point $P$ is any point on circle $C$: $x^{2}+y^{2}-8x-8y+28=0$, curve $N$: $x^{2}+4y^{2}=4$ intersects with the $x$-axis at points $A$ and $B$. Line $OP$ intersects with curve $N$ at point $M$. The slopes of lines $MA$, $MB$, and $OP$ are denoted as $k_{1}$, $k_{2}$, and $k_{3}$, respectively. Determine the range of $k_{1} \cdot k_{2} \cdot k_{3}$.

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