
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 an ellipse $C: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a>b>0)$ passing through point $M(1, \frac{3}{2})$, with its left focus at $F(-1,0)$.
(1) Find the equation of ellipse C.
(2) Given that line $y=kx+2$ intersects ellipse C at two distinct points $P$ and $Q$, and point $N(0,-2)$, let the slopes of lines $NP$ and $NQ$ be $k_1$ and $k_2$ respectively. Find the range of values for $k_1 \cdot k_2$.

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