
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 $f(x)=x+\frac{4}{x}$ and $g(x)=2^{x}+a$, for all $x_1\in\left[\frac{1}{2},1\right]$, there exists an $x_2\in[2,3]$ such that $f(x_1)\geqslant g(x_2)$. Determine the range of values for the real number $a$.

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