
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 $C$ with foci $F_{1}(-2\sqrt{2}, 0)$, $F_{2}(2\sqrt{2}, 0)$, and a moving point $P$ on it satisfies $|PF_{1}|+|PF_{2}|=4\sqrt{3}$. Let point $O$ be the origin, and the lower vertex of ellipse $C$ be $R$.
(Ⅰ) Find the standard equation of ellipse $C$;
(Ⅱ) Suppose a line $l_{2}$ passing through the point $(0, 1)$ with slope $k$ intersects ellipse $C$ at points $M$ and $N$, investigate whether $\overrightarrow{RM} \cdot \overrightarrow{RN}$ is always a constant value regardless of the value of $k$. If yes, find the constant value; if not, explain why.

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