
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 $f(x)=x+a$ and $g(x)=x+ \frac {4}{x}$, if for every $x_{1} \in [1,3]$, there exists $x_{2} \in [1,4]$ 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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