
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]


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Given that $n$ is a positive integer, the graph of the quadratic function $y=2^{2n}x^{2}-6\cdot 2^{n}x+8$ is a parabola. If the length of the segment intercepted by this parabola on the $x$-axis forms a sequence $\{d_{n}\}$, then $\lim_{n→∞}({{d_1}+{d_2}+⋯+{d_n}})=$____.

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