
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 every $$x_{1} \in \left[ \frac {1}{2}, 3\right]$$, determine the range of the real number $a$ such that there exists an $$x_{2} \in [2, 3]$$ satisfying $$f(x_{1}) \geq g(x_{2})$$.

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