
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 functions $f(x)=x+\frac{4}{x}$ and $g(x)=2^{x}+a$, if for all $x_{1}\in [\frac{1}{2}, 1]$, there exists $x_{2}\in [2,3]$ such that $f(x_{1})\geq g(x_{2})$, find the range of real number $a$.

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