
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 the functions $f(x)=x+ \frac{4}{x}\;,\,g(x)=2^{x}+a$, for all $x\_1\in\left[\frac{1}{2}\,,\,3\right]$, find the range of the real number $a$ such that there exists $x\_2\in[2,3]$ satisfying $f(x\_1)\geqslant g(x\_2)$.

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