
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 $\Gamma$: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ that passes through point M ($-2$, $1$), and its right focus is at $F( \sqrt {3}$, $0)$.
(I) Find the standard equation of the ellipse $\Gamma$;
(II) Line AB passes through point N ($1$, $0$) and intersects the ellipse $\Gamma$ at points A and B. Let $t= \overrightarrow {MA}\cdot \overrightarrow {MB}$. If the maximum and minimum values of $t$ are $t_{1}$ and $t_{2}$ respectively, find the value of $t_{1}+t_{2}$.

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