
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 $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ with its left and right foci being $F_{1}$ and $F_{2}$ respectively, eccentricity $e= \dfrac { \sqrt {2}}{2}$, and passing through the point $(1, \dfrac { \sqrt {2}}{2})$,

$(1)$ Find the standard equation of the ellipse;  
$(2)$ A line $l$: $y=k(x+1)$ intersects the ellipse at points $M$ and $N$, and $| \overrightarrow{F_{2}M}+ \overrightarrow{F_{2}N}|= \dfrac {2 \sqrt {26}}{3}$. Find the equation of line $l$.

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