
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 $g(x)=2^{x}+a$, if for all $x_{1} \in \left[ \frac{1}{2},1 \right]$, there exists $x_{2} \in \left[ 2,3 \right]$ such that $f\left( x_{1} \right) \geqslant g\left( x_{2} \right)$, then the range of the real number $a$ is ______.

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