
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 $C$: $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ with eccentricity $\dfrac {1}{2}$, and a line $l$: $x+2y=4$ that intersects the ellipse at exactly one point $T$.

$(I)$ Find the equation of the ellipse $C$ and the coordinates of point $T$;  
$(II)$ Let $O$ be the origin, and a line $l′$ parallel to $OT$ intersects the ellipse $C$ at two distinct points $A$ and $B$. The line $l′$ intersects the line $l$ at point $P$. Determine whether $\dfrac {|PT|^{2}}{|PA|\cdot |PB|}$ is a constant value. If it is, find the constant value; if not, explain why.

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