
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 that $a\_n$ is the coefficient of the $x^{2}$ term in the expansion of $(2+x)^{n}$ $(n∈N^{},n≥slant 2,x∈R)$, find the limit: $\lim\_{n→∞}( \frac {2^{2}}{a_{2}}+ \frac {2^{3}}{a_{3}}+…+ \frac {2^{n}}{a_{n}})=$ _____ .

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