
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
For the function $f(x)=x-\frac{2}{x}, x∈[1,2]$, and $g(x)=-{x}^{2}+ax-5$, for any $x_{1}\in \left[1,2\right]$, there always exists $x_{2}\in \left[2,4\right]$ such that $g(x_{2})\leqslant f(x_{1})$ holds. Find the range of values for $a$.

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